QUESTION:
Most physicist say that an antimatter engine is impossible because there is no way to store the antimatter but if you were able to get raw positrons and electrons and store them in seperate electrically charged tanks (each with the same charge as the particle they are holding). would you be able to sucessfully store the matter and antimatter and decide when to open it and close it. So basically is the atraction between matter and antimatter stronger than the electroweak force?

ANSWER:
If you have a hollow conducting tank and charge it up with electrical
charge, the field inside is zero, so your plan to store charge inside
will definitely not work; the only force felt by the charges inside will
be the forces between those charges which will have the effect of
pushing them all out to the tank. All the positrons in the positron tank
would annihilate with electrons in the tank; all the electrons in the
electron tank would end up on the outer surface of the tank. And, by the
way, the only force between an electron and a positron is electrostatic.

QUESTION:
I have been reading a lot lately about the prospects of nuclear fusion reactors; especially regarding electrical power plants. My question is this: if the hot plasma from the reaction is shielded from the equipment to protect it from the heat by a magnetic bottle, how then do you access the heat to make electrical power via steam for turbine generators or direct conversion from heat to electricity.

ANSWER:
The purpose of the magnetic bottle is to keep the hot plasma isolated
from the physical containment; just touching the containment vessel
would present two problems—it would cause instabilities in
the plasma and it would damage the vessel. But the plasma is hot and
anything hot will radiate heat energy; in other words, the magnet bottle
contains the plasma, not the heat. This radiant heat would rapidly heat
up the vessel which would heat up some coolant mechanism (imagine having
water tubes coiled around the outside of the vessel) which would carry
away the heat to drive the turbines.

QUESTION:
why are sparks more likely to occur between two charged particles closer together rather than far.

ANSWER:
For air to become a conductor, there must be a sufficiently strong
electric field to ionize the air molecules. There must therefore be a
potential difference (voltage) between the two electrodes. The air has a
dielectric breakdown strength of about 30 kV/cm which means that 30,000
V are needed for a gap of 1 cm but only 3000 V is needed for a gap of
1mm.

QUESTION:
If a capacitor is made of oppositely charged plates, why do they look like cylinders inside computers, remote control cars and other electronics

ANSWER:
The easiest form of capacitor to understand and analyze in an
introductory physics class is the parallel plate capacitor. But any two
conductors insulated from each other is a capacitor. One possible
capacitor is a wire along the axis of a hollow cylinder, but that is not
what the common capacitor you are referring to is. Rather, it is a parallel
plate capacitor! The analysis of the capacitance of two parallel plates
shows that the capacitance is proportional to the area of the plates and
inversely proportional to the distance between them. So, take a two
ribbons of foil as long as a football field to make the area big and
separate them by sandwiching a ribbon of mylar between them to make the
separation small; then just roll it up so you can fit it in your device!

QUESTION:
When I had solar panels installed on my house the old fashioned meter ran backwards when the Sun was bright. They have now fitted a digital meter which can sense when energy is being sent into the grid. I can see how this could be done with DC, but how does it work with AC? In AC the current is switching direction at 50 Hz. How can the meter sense the 'direction' of the energy flow?

ANSWER:
You are right, the average current is zero. However, the current is not
the power —the power is the product of the current and the
voltage. Both current and voltage are sinusoidal functions of time,
i (t )=I sin(ωt ) and v (t )=V sin(ωt+φ ),
so p (t )=IV sin(ωt )sin(ωt+φ ).
The graph above shows three choices for the phase φ between
i and v . For φ=π /2 the time average of
the power is zero, no energy flow; for φ=π and φ= 0
the time average of the power is negative and positive, respectively.
The motor in a mechanical meter turns in opposite directions for
different signs of the average power; in a digital meter the average
power is determined by an electronic circuit.

FOLLOWUP
QUESTION:
Thank you for your reply to my question about the power direction with energy generated by solar panels. I now understand that phase angles are crucial.
The inverter in the loft takes DC from the panels and converts it into AC. To feed energy back into the grid does the inverter have to deliberately adjust the phase or does this occur naturally when there is an excess of energy?

ANSWER:
All that matters is what the phase is at the meter. If energy is flowing
into your house the phase will be one way, if flowing out it will be the
other.

QUESTION:
Is there a law in physics that allows me to calculate the magnetic field at a certain point created by a charged particle moving in a straight line
with constant speed in empty space?

ANSWER:
Yes, there is an equation. I will warn you, though, that this is quite
technical and pretty high-level. Refer to the figure to the left. The
charge q , with velocity v is at
position x (t ) at time t ; we
wish to know the field at position r at time
t . However, since the information about the field propogates at
the speed of light, c , the field at time t is
determined by where the charge was at some earlier time t _{ρ} ;
|r -x (t _{ρ} )|≡|ρ |=ρ =c (t-t _{ρ} ).
After much calculation (see the detail in Chapter 10 of David Griffith's
book
Introduction to Electrodynamics ), the magnetic field is
B (r ,t )=(v xE (r ,t ))/c ^{2
} where the electric field is
E (r ,t )=[q /(4πε _{0} )][ρ /(ρ ·u )^{3} ][(c ^{2} -v ^{2} )u ];
the vector u is defined as u ≡c1 _{ρ} -v
where 1 _{ρ} is a unit vector in the
direction of the vector ρ .
For high
speeds, the fields look like the diagrams below.

A DDED
NOTE:
The above expressions for electric and magnetic field are exactly
correct. You can write approximately correct equations for particles
with speed much less than the speed of light, v<<c :
E (r ,t )=[q /(4πε _{0} )][(r -x )/|r -x |^{3} ]
and
B (r ,t )= [ qμ _{0} /(4π )][ v x(r -x )/|r -x |^{3} ].
These are simply
Coulomb's law and the
Biot-Savart law .

QUESTION:
Why do moving charged particles respond to magnetic fields? I know that every charged particle has it's own magnetic field and permanent magnet will attract/repel these particles, but the force will be so little that it won't be able to be measured at all, but when it comes to moving, a "magic" happens, and I don't understand what is special with moving charges versus stationary charges.
Does the magnetic field between magnet and charged particle increase proprtional to velocity and the force gets noticable? In turbines, when magnet is rotating, how that makes electrons move?
Why are those electrons affected by magnetic field at all? There is Lorentz law but how was that
equation figured out? Does that equation only depend on experiments? Did they just see that electrons start moving when we rotate magnet next to them and that's all?

ANSWER:
Site groundrules specify single, concise, well-focused questions so I
should have just thrown this out. Instead I have edited the question a
bit to make it more focused. There is no way I can fully answer the
questions because they really ask that I give you a full course in
magnetostatics. First of all, disabuse yourself of your second sentence.
All charged particles do not have a magnetic field if they are not
moving; true, most elementary particles (electrons, protons, etc .)
have magnetic moments, but these are incredibly weak and do not normally
react to a magnetic field; if you just have an electric charge Q ,
it experiences zero force if at rest in a magnetic field. Yes, it is an
empirical fact (experimentally observed) that a charged particle Q
with velocity V in a magnetic field
B experiences a force F =QV xB .
It is now understood that there is only one field, the electromagnetic
field, and electromagnetism is a relativistic theory; it is, though, no
longer a vector field like you are familiar with, but a tensor field
with nine components. What this means is that the answer to your
question about there being electrons at rest with a magnet moving is
that an electron moving in a static
field is no different from an electron at rest and the magnet moving;
that, essentially is relativity—all that matters is relative
velocity. Also, once you understand that there is a single field, the
Lorentz force arises naturally.

QUESTION:
Can an electric current flowing in a wire be stopped by a magnetic field? If so, how?
I need to stop it from distant.

ANSWER:
The magnetic force on a moving charge is always perpendicular to
its velocity. To stop a moving object you must apply a force
antiparallel to its velocity.

QUESTION:
A quantity of electrical energy is defined by volts x amps x time. A quantity of mechanical energy could be defined (or is) by force x distance which equates to kinetic energy. When electrical energy is converted into mechanical, a force can be created by applying voltage and current (amps). Is this a paradox? Electrical energy is functionally force x time while mechanical energy is force x distance.

ANSWER:
1 V=1 J/C and 1 A=1 C/s, so 1 volt ·amp·second=1
Joules=force·distance. No discrepancy, no paradox. Another way to
look at this is that current times voltage is power and power is W=J/s.

FOLLOWUP QUESTION:
I totally understand that 1 amp is 1 coulomb per second. I don't know where 1 volt is equal to 1 joule per coulomb comes from or why that is true.

ANSWER:
The electric field E is defined to be the force F
felt by a charge Q divided by Q . The electric
potential V is defined as E times distance d
over which it acts. V=Ed=Fd /Q =[J/C]

QUESTION:
magnetic force on charge q moving with velocity v =qV x B if i observe this charge from a car moving with same speed and direction as that of q than it velocity as observed by me will be 0 so the force will be 0.i am not able to understand this dilemma at one time force non zero and at other time it is 0

ANSWER:
The problem is that the electric and magnetic fields in one frame of
reference are not the same as in another moving frame. (This is special
relativity.) In your case you first start with a magnetic field and zero
electric field. Suppose that the magnetic field is in the y -direction,
B =j B , E =0,
and the velocity of q is in the x -direction, v =i v .
Then the force would be F =k qvB
in the z -direction. In the moving frame the new fields would be
B' =j γB and E' =k γvB ,
where γ= 1/ √(1-(v /c )^{2} ).
Note that
E' =v x B' ;
therefore the force, as seen in the moving frame is F' =qE' =qv x B' =k γqvB ,
as you would expect. Note, however, that F' ≠F
, they differ by a factor of
γ ; this is because force is said to be not
Lorentz invariant
and it is not really a useful quantity in relativity.

QUESTION:
If I use some magnetic bars, cut them perfectly so that I can put them together to form a globe, with the same pole pointing outwards, and the other pole pointing inwards, do I get a Magnetic monopole object?

ANSWER:
Think of your bars as dipoles of positive and negative magnetic charges
(monopoles) separated by a distance d . The magnitude of the magnetic
field B of a monopole is inversely proportional to the square of the
distance r from the charge, B=kq /r ^{2} where
k is some constant. In the drawing above the field at point p is B=B _{-q} +B _{+q} =kq [(1/(r-d )^{2} -(1/r+d )^{2} ]=4kqrd /[(r+d )^{2} (r-d )^{2} ].
Now, look at the field when r>>d : B ≈4kqd /r ^{3} .
The field does not look like a monopole because it falls off like 1/r ^{3} ,
not 1/r ^{2} .

QUESTION:
Suppose I have a charge +q and there is a point P , Suppose I place a conductor between the charge +q and P . Since there are free electrons in it , Negative electrons move towards +q and equal positive charge inside the conductor near P , The conductor has charge distribution like a dipole. So If I want to calculate E field at P . I could use superposition principle to find E at P due to +q and E due to dipole. But Gauss's law says that dipole doesn't contribute anything to E field at P. Can you explain me 'intuitively' (Not in equations) why the dipole wont contribute anything to the field at P ?

ANSWER:
Gauss's law does not say that the dipole contributes nothing at P. If you
put a spherical Gaussian surface enclosing both q and point P the net
charge enclosed is q but that does not mean that the field due to the
dipole is zero everywhere on that surface. All you can say is that the net
electric flux passing through that surface is q / ε _{0} .
Gauss's law is usually useful in determining a field only if the field can
be argued to have constant magnitude and normal to the surface everywhere.
Superposition, not Gauss's law, should be used for this problem.

QUESTION:
Sir,I am a mechanical engineer by profession but very interested in reading physics fundamentals. Recently I went through the fundamentals of electro magnetism and I got this doubt. Consider two charges each of charge +q rigidly fixed in a train moving with a constant velocity, V. Let the train speed be negligible compared to speed of light so that we can treat the problem in non-relativistic terms. The fixity condition ensures that it overcomes electrostatic forces and remain motionless. A traveler in train sees both of them at rest and there wont be any magnetic forces developed between the charges.
Now consider an observer in platform. For him, both charges are moving with a constant velocity, V equal to the train velocity. Each charge will develop magnetic field according to this observer as per Biot-Savart law and there will be mutual attraction as each charge is moving under the magnetic field of other.Thus, an observer in train sees no magnetic forces whereas an observer in platform sees mutual magnetic attraction. How do you explain this?

ANSWER:
There is no rule which says that the either the electric or magnetic field
must be the same in all frames of reference, even slowly moving frames like
you specify. The real root of your problem is that electromagnetism is
intrinisically relativistic, even at slow speeds; the electric and magnetic
fields of classical electromagnetism are really both components of the
electromagnetic field which is a tensor and when you change inertial frames,
you cause a transformation of that tensor into another where both the
electric and magnetic field pieces of it are different. In your second case
you would also find that the electric fields were slightly different from
their original values but the differences would be very tiny; the magnetic
fields, though, are nonzero but small, but small is very big compared to the
original magnetic field of zero.

If you
are interested, I will give here the electric and magnetic fields for one of
the charges moving with velocity v in the +x direction.
E' =i E_{x} + γ (j E_{y} +k E_{z} )
and B' =- (v xE' )/c ^{2
} where
γ= 1/√[1-(v /c)^{2} ] and i , j ,
k are unit vectors; the vector E is in the frame
where q is at rest and E' and B' are when
q is moving.

QUESTION:
Suppose we have a horseshoe magnet. Now we bend it in such a way that it becomes doughnut shaped and poles remain in contact with each other. In this situation what will happen to the magnet? Will it behave as a magnet? Where would be its poles? What will happen to domains inside the magnet?

ANSWER:
A horseshoe magnet is just a bent bar magnet, so let's start there. I have
shown a short stubby bar magnet, but you can imagine that as it gets longer
relative to its width the field inside will get more and more uniform. Now,
bend it around into a circle and it will look just like a toroid. The
magnetization inside will remain pretty much the same as before you bent it
and there will just be field inside the torus, not outside. The domains will
all stay pretty much the same.

QUESTION:
I've started reading an elementary particle textbook and it doesn't explain why a moving charged particle radiates an EM field. I was hoping you could help with that.

ANSWER:
The semantics of "radiates an EM field" is somewhat ambiguous. A charged
particle at rest creates a static electric field. A charged particle
moving with constant velocity (constant speed in a straight line) creates
both an electric field and a magnetic field and both change with time. But
neither of these situations are said to radiate electromagnetic
fields. Electromagnetic radiation propogates through space as waves; visible
light, for instance, is an electromagnetic wave. Electromagnetic fields can
be created when a charged particle accelerates. E.g., an antenna radiates
radio waves when electrons in the antenna are made to oscillate back and
forth (accelerating). The derivation of how accelerating charges radiate is
a topic in an intermediate E&M course and beyond the scope of this site.

QUESTION:
Magnetic flux according to my book is total no. of magnetic field lines passing through a given area in magnetic field. ok but why there are not infinite no. of magnetic field lines, because magnetic field line are defined as the path that a magnetic north monopole would take if left in north part of magnet, so if i take a monopole and leave one atom away from the previous position then it should take a slightly different path and that path should be considered as magnetic field line,so in this way i can draw millions of line.

ANSWER:
Magnetic flux is well defined:
Φ _{M} ≡∫∫B · dA ,
the area integral of the magnetic field. If the integral is over a closed
surface, the flux is zero; this is the famous situation which tells you that
there are no point sources (called magnetic monopoles) of magnetic fields
like there are for electric fields. If you like, you may interpret this as a
number, but that is not really fundamental. If you talk about uniform
magnetic fields which are perpendicular to a plane surface, Φ _{M} =BA
, is the flux through an area A . Then, if you interpret
Φ _{M}
as a number, you would simply say, for example, there were 10 lines through
an area of 1 m^{2} if the magnetic field is 10 T. You could ask the
same question about electric flux,
Φ _{E} ≡∫∫E· dA .
This is perhaps a little easier to understand because you can have point
charges. For example, if you have a 1 C point charge, the electric field 1 m
from it is E=Q /(4 πε _{0} r ^{2} )=1/(4x3.14x8.85x10^{-12} x1^{2} )=9.27x10^{9}
N/C. The flux at a distance of 1 m from the charge would therefore be Φ _{E}
=EA = 9.27x10^{9} x4x3.14x 1^{2} =1.17x10^{11}
Nm^{2} /C. Incidentally, this is the flux regardless of where you
measure it because the area of the sphere
(4 πr ^{2} )
surrounding the point charge appears both in the denominator of the field
and in the numerator of the flux and cancels. Hence, you could say that
there were 1.17x10^{11} lines of
electric field emanating from a 1 C point charge. You can see this from
Gauss's law,
Φ _{E} =∫∫E · dA =Q /ε _{0}
if the integration is over a closed surface enclosing the charge Q .

QUESTION:
Do permanent magnets have an electric current surrounding them?
Permanent magnets seems to have different properties to electromagnets, such that electromagnets can be used for induction and energy transfer if a conductor is placed within their changing magnetic field.
So I understand that an electromagnet will have a changing magnetic field, which in turn generates a changing electrical current in a conductor placed within this magnetic field.
My question is, do permamant magnets generate this same electric current if a conductor is placed within their magnetic field?
I.e. if I had a strong permanent magnet, would I be able to generate a current in a coil if it was brought into the permananet magnet's magnetic field?

ANSWER:
A permanent magnet may be thought of as having "bound" currents. These are
not currents you could actually connect an ammeter to and measure. If you
are interested, there are, in general, two types of bound current, bound
volume current density J _{b} and bound surface current
density K _{b} . If the magnetization of the material is
M , you can write J _{b} =curlM
and K _{b} =M xn where
n is a unit vector normal to the surface and pointing out of the
volume. I do not understand any of your rambling about induction. I will
simply say that any changing magnetic field can induce currents and a
permanent magnet is a source of a magnetic field; moving that magnet,
through a wire ring, for example, will induce a current in the ring.

QUESTION:
Why is the direction of magnetic
field lines outside the magnet from north to South and not South to North?
Is it a convention or has got a logic behind it?

ANSWER:
It is just as arbitrary as whether a electrons are negative or positive or
whether an electric field points toward or away from a negative charge. If
you chose the different direction from conventional, you would have to use a
left hand rule to determine the force on a positive charge moving through a
magnetic field.

QUESTION:
Just a question regarding forces
acting equal and opposite directions... Let's say an electron is traveling
through space with nothing around it for thousands of kilometers and it
passes through a magnetic field (or electric field). The source of that
field is light years away let's say. The electron will experience a force on
it causing its trajectory to change.
My question is if the electron is experiencing a force then what is the electron exerting a force back onto?
I'm a bit stumped by this.

ANSWER:
The answer is that Newton's third law, applied simplistically, is not likely
to work for charged fields moving in electric or magnetic fields. A simple
example is given in an older
answer . This does not mean that
Newton's third law is wrong, it is simply that just by saying two forces are
equal and opposite, you have to be more general, particularly when
velocity-dependent fields (like the magnetic field) are present.
Essentially, Newton's third law is equivalent to momentum conservation; if
two isolated objects collide, their momentum would not be conserved if the
forces they exerted on each other were not equal and opposite. Thus, in that
earlier answer , the total
linear momentum of the two interacting charges would not remain constant.
But the catch is that these two particles are not the only things around,
their fields are also present; it turns out that the fields have linear
momentum densities and if you also include this linear momentum in the
problem, the total momentum is, indeed, conserved. This sort of gets beyond
the "layman" philosophy of this site to pursue this more quantitatively.

QUESTION:
Dropping a 3/4 inch sphere magnet
through a 3/4 inch copper tube creates an electrical field, (Lenz's Law) If
you suspend some magnets in the copper tube using opposing poles, does this
continually create an electrical field?

ANSWER:

Lenz's law applies only if the magnetic field is changing. If you simply
have a magnet suspended there there will be no induced electric field.
You might as well hang it from a string or hold it up with your finger,
if the magnetic field does not change Lenz's law is not applicable.

QUESTION:
A hollow charged conductor has normal electric field on its outer surface , why?

ANSWER:

In an ideal conductor, some of the electrons are free to move. If any
electric field at the surface of a conductor had a component parallel to
the surface, electrons would accelerate along the surface and you would
not have an electrostatic situation.

QUESTION:
Why do materials with static electricity attract substances that are not charged?

ANSWER:

I will assume that the charge on the charged object is positive. If the
uncharged object is a conductor where electrons are free to move,
electrons will tend to migrate to the surface closest to the charged
object leaving a positive charge on the opposite side; since the
electrons are closer to the charged object than the positive charge,
there will be a net attractive force. If the uncharged object is a
conductor where electrons are free to move, electrons will tend to
migrate to the surface closest to the charged object leaving a positive
charge on the opposite side; since the electrons are closer to the
charged object than the positive charge, there will be a net attractive
force. If the uncharged object is a nonconductor with electrons not free
to move, each atom or molecule in the uncharged object, seeing the
electric field from the charged object, will become polarized (see
picture above) such that the negative side will be closer to the charged
object, again resulting in a net attractive force.

QUESTION:
Charges concentrate on sharp points of an object. Voltage proposionates to charge/radius. In an egg shape object the voltage equal everywhere . But charges are high where the radius is small. How is it possible?

ANSWER:

Electric field at the surface of an ideal conductor is always normal to the
surface regardless of the charge distribution. This means that it takes
no work to move a charge on the surface. By definition, therefore, the
surface is an equipotential.

QUESTION:
if I take a uniformly charged non conducting spherical shell then electric field intensity inside the shell is zero (gauss law) but then I put a unit positive charge outside the spherical shell then even as there is no net charge inside the spherical shell so by gauss law electric field must be zero but as shell is non conductor there cant be a new arrangement of charge on shell take place so without a new arrangement how can electric field due to outside charge be neglected?

ANSWER:

No, you cannot just choose a Gaussian surface and say there is no field
inside it just because there is no charge inside it. You can only
conclude that the net electric flux into the surface and the net flux
out are the same. If the charge distribution is spherically symmetric
(as it was before the extra charge was added), Gauss's law can be used
deduce zero field inside.

QUESTION:
Is this a good way to explain Lenz's law moving magnetic field around a conductor can produce a current. This current is opposing the magnetic fields that created it.

ANSWER:
No, that is not a good way. The induced current tends to have a
field which opposes the change in the magnetic field which created
it. For example; if the inducing field is increasing, the induced field
would be in the opposite direction, and if it were decreasing, the induced
field would be in the same direction.

QUESTION:
I am very curious - do different electromagnetic waves/frequencies affect each other in any way? If one photon hits another or if they pass each other, do they affect each other in any way? For instance, if I have a flashlight with a stream of light, and another flashlight with a stream of light shining perpendicularly through the first one, I know that the streams do not seem to affect each other in any way - but do they? In ANY way?

ANSWER:
Indeed, photons interact with each other. However, for all
practical purposes, two flashlight beams are not sufficiently intense for
there to be an observable rate of interaction. Physicists do study the
interaction between
two photons ,
though. One well-known example is the interaction of a high-energy photon
with the electric field of a nucleus (and therefore a photon) to create an
electron-positron
pair .

QUESTION:
Why does the electric field at infinite distance from a uniformly charged disc not equal to that of a point charge as it is zero.

ANSWER:
I do not understand. Any local charge distribution (not, itself,
extending to infinity) goes to zero at infinity. What matters is how
it goes to zero. At very large r , the field should go to zero like
Q /r^{2} where Q is the net charge, and I guarantee that a
uniformly charged disc will do this. If the net charge is zero, it will
approach zero differently. For example, an electric dipole field will
approach zero like 1/r ^{3} .

QUESTION:
How can two metallic objects having same but opposite charges (one loses electrons and one gain electrons) and we know that metals have the ability to lose electrons only?

ANSWER:
Actually, metals can form negative ions. But, that is beside the
point. Electrons could be added to a conducting object and they would stay
there even if they were in no way bound to atoms. The reason is that in a
conductor, if you try to remove an electron from it, a virtual mirror image of the
electron is formed which binds it. The energy necessary to remove the
electron is referred to as the work function of the metal.

QUESTION:
Does the AC current has a DC part?

ANSWER:
It can have if the time-averaged current is not zero.

QUESTION:
Suppose we have a thick spherical metallic shell with a spherical cavity inside. A charge is placed at any point in the cavity except for the centre of the sphere. Now how do we find the potential of outer surface of the shell? My friend says that no matter where we place the charge inside the cavity, the potential will be the same, as if it is placed at the centre. But
he does not have any logical proof to the statement. Is he right? Then what is the proof? If not, how do we go on calculating the potential?

ANSWER:
This question can be answered in a purely conceptual way.
Because the electric field in the conductor must be zero and the induced
charge on the outer surface must be Q (the same as the point charge),
the surface charge distribution must be uniform. In fact, the conductor and
the cavity do not even need to be spherical for the field outside to be
independent of the position of the charge inside.

QUESTION:
In the Meissner effect; when the falling bar magnet's descent is arrested due to the magnetic impermeability of the supercooled lead dish toward which it is falling, what happens to its inertia? Does the field around the bar magnet deform and absorb it, or does something else occur?

ANSWER:
It is essentially the same as if the magnet were attached to an
unstretched spring (no superconductor) and dropped; as the magnet falls, gravitational
potential energy decreases and spring potential energy increases but faster. The magnet
will speed up until eventually you reach a point (equilibrium point) where
the force from the spring (up) is the same as the weight of the magnet (down)
and then it slows down, eventually going back up and so on. Because there are
drag forces (air drag and the damping in the spring) it settles down to the
equilibrium point. In the Meissner effect, the magnetic field of the magnet plays
the role of the spring in my simple analogy. Because the superconductor
excludes the field, the field deforms as the magnet falls and pushes back up
harder on the magnet as it gets closer to the superconductor which means
that the energy of the field is increasing. You were essentially right in
your speculation that "�the
field around the bar magnet deform[s] and absorb[s]�"
the kinetic energy.

QUESTION:
Is it true that even an electron has its north and south poles; if it
is, then how?

ANSWER:
A simple bar magnet (shown blue) has a magnetic field shaped as
shown by the right-most figure to the right. What is fundamental is the
shape of the field, not the N and S poles of the bar. This is called a
magnetic dipole field. To the left of this is the magnetic field caused by a
current loop. Notice that this little current loop has a very similar field
shape, so you could identify its N and S poles. An electron has an angular
momentum, that is it is spinning. A spinning ball of electric charge is like
a stack of tiny current loops, so it will also have a dipole-shaped field.
Therefore you could say that an electron has a north and south pole.

QUESTION:
The definition of "electric current" I find in my school books is: "directed flow of electrons". The power stations here in my country use hydro power to make work some huge generators which create electricity, i.e directed flow of electrons. But their functioning is not based in obtaining electrons from something (not the water nor the metal), instead its function is to create some magnetic fields which seem to be essential in creating electric current.
My question: Is the above definition of electric current correct? If yes, where do the continuous flow of electrons come from? Are really magnetic fields a limitless source of electrons, if not, how do they generate limitless electricity?

ANSWER:
The electrons which flow in a wire were already there
before the current started. In materials which are conductors there are
electrons which are very easy to move around. Magnetic or electric fields
may be used to cause these "conduction electrons" to move. Electrons are not
being injected into the wire.
QUESTION:
Is there a magnetic field or not?
If there is a charged particle with no velocity relative to viewer A there is no current and no resultant magnetic field, right? But if the same particle is viewed by another observer moving at some velocity relative to it then it could be said the particle is moving at -v and should show both a current and magnetic field.
How can you reconcile this?

ANSWER:
Let me pose an analogous question. Is there a velocity or
not? If there is a particle with no velocity relative to viewer A there is
no velocity, right? But if the same particle is viewed by another observer
moving with some velocity relative to it, then it could be said that the
particle is moving with some velocity. How can you reconcile this? Like most
observables in nature, magnetic fields depend on the frame from which they
are observed and, in some special cases like your example, you can actually
find a frame in which the magnetic field is zero. In your example, if the
observer moves with speed 100v , the magnetic field will be much
stronger than if he moved with speed v . Electric fields also behave
this way and the electric field observed by the moving observer in your
example will differ from the field seen in the frame where the charge is at
rest. Actually, there is only one field, the electromagnetic field; the idea
of separate electric and magnetic fields is a historical artifact. You might
be interested in a similar question about
electromagnetic radiation fields .
QUESTION:
Why is it that hot objects such as lightbulb filaments emit light while cold objects such as ourselves emit no light at all?

ANSWER:
Well, let's first define "light" as any electromagnetic
radiation, not just the visible spectrum. All objects radiate light and the
wavelengths they predominantly radiate depends on temperature. A human body
has a temperature around 300 K (80^{0} F) and a tungsten filament has
a temperature of around 3000 K (5000^{0} F). The picture to the right
shows the radiation for both of these temperatures; also note the visible
spectrum indicated by the colored vertical bands near 0.7 microns. At 3000
K, the radiation is most intense in the region of visible light; at 300 K
there is almost no intensity of visible light and the spectrum is most
intense around 10 microns which is in the "invisible" infrared spectrum.
Night vision goggles are sensitive to infrared radiation and enable you to
see "cold" objects in dark situations.
QUESTION:
It is said that charges are quantised.Also if we bring two identical solid
conducting spheres in contact with each other,their charges are equally
distributed among them. Now suppose if we have a body A with -5e charge and
body B with 0 charge.Now what will be the charge distribution between the
bodies if we bring them in contact and then separate them?Since charges are
quantised,we cannot have 2.5-2.5 distribution.So will it be 3-2 or 2-3
distribution or what?

ANSWER:
The rules you learn like the one you quote apply only
when the charge can be thought of as a continuous fluid which can spread
itself out on any surface, no matter how large, and have zero thickness.
Because the electron charge is so small, these rules work very well to
describe electrostatics for normal circumstances. Obviously, a case like you
describe, with 5 excess electrons is in no way like a fluid and I would
guess that anything from 5-0 to 0-5 could be the distribution over a time.
In principle, the 5 electrons would arrange themselves so that each was as
far away from the other 4 as possible, but there would not be a unique such
distribution.
QUESTION:
Would it be possible to suspend an electron via electrostatic levitation in
a uniform magnetic field? And if the voltage was decreased enough so that
the electrostatic force on the electron was lower than the force due to the
electron's weight would the electron then experience a 'fall' due to
gravity?

I'm asking this because I'm wondering if placing a positron in a uniform
magnetic field (in a vacuum) and lowering the voltage to a very small value
so that the electrostatic force is lower than the weight would cause a
positron to also experience a 'fall'. And if it did experience a fall it
could be ascertained whether it would fall upwards or downwards.

I'm 17 years old and in the UK about to study physics at university in september and was just curious about this since one of our topics this year was electrical phenomena and we talked about millikan's oil drop experiment which featured a similar sort of suspension when the electrostatic force and force due to gravity were balanced.

It's a thought I had when wondering if antimatter
was affected by gravity the same way matter is.

ANSWER:
It is always nice to see young folks asking interesting
questions. First, I need to correct one thing: everywhere you refer to a
"magnetic field" you should say "electric field"; a magnetic field exerts no
force on a charge at rest which is what you want to observe, � la
Millikan. Now, it is known to extraordinary precision that the inertial mass
of a positron is equal to the inertial mass of an electron. By inertial mass
I mean the ratio of the force you apply to it divided by its acceleration,
in other words its resistance to being accelerated. (A more correct way,
relativistically, to say this would be that they have equal momenta for
equal speeds.) I believe it is true that nobody has ever "weighed" a
positron by measuring the force it experiences in a gravitational field.
But, if the gravitational mass were different from the inertial mass, this
would fly in the face of the theory of general relativity. But, let's talk
about the feasibility of your experiment. The mass of an electron is about
10^{-30} kg so its weight would be about 10^{-29} N (taking
g ≈10 m/s^{2} ). The electron charge is about 1.6x10^{-19}
C and so the electric field required to levitate an electron would be 10^{-29} /1.6x10^{-19} ≈6x10^{-11}
V/m. Suppose we use a parallel plate capacitor to create this field. The
charge density σ on a plate with field E is about σ=ε _{0} E≈ 10^{-11} x6x10^{-11} =6x10^{-22}
C/m^{2 } which would correspond to an electron density on the plates
of about 6x10^{-22} /1.6x10^{-19} ≈ 0.004
electrons/m^{2} ! This would correspond to about one electron for
every 250 square meters! That would not give a very uniform field would it?
There is no such thing as a uniform surface charge density because charges
in nature do not comprise a continuous fluid; so really tiny uniform fields
are not possible. I did all that just for the fun of it, but there is an
even more serious consideration�the earth itself has an electric field near
the surface of typically 100 V/m pointing down, so an electron would be
repelled upward. To do your experiment you would have to get rid of that
field and I do not believe that it would be possible to be assured that you
could make the residual field much less than your
6x10^{-11} V/m. Back to the drawing board! Keep asking those hard
and interesting questions, though, and good luck with your university
studies.

ADDED
NOTE:
A
recent article discusses a new proposal to compare matter and antimatter
weights.

QUESTION:
Why is charge a scalor quantity if different charges are given positive and negative signs and also if the flow of current which is mainly due to the flow of electrons but has direction,by convention,same as that of protons??

ANSWER:
What makes you think that a scalar quantity cannot have a
sign? How about Celsius temperature, -40^{0} C or +20^{0} C?
How about time, -5 s is 5 seconds before t =0. The fact that electrons
have negative charge is just an accident of history. All important aspects
of electromagnetism would be just the same if you called the electron charge
positive. The reason that current is defined to flow in the direction of
positive charges has to do with the definition of
current density
which is a vector quantity.

QUESTION:
My son and I are trying to build a Foucault pendulum. We have 11' ceilings so we need to dampen ellipsoidal motion and provide a drive mechanism to keep the pendulum moving. I've seen pendulum driver circuits that operate via magnetic induction with relays, transistors, etc. but do not prefer these; it's not clear that the pendulum and Earth are doing the magic, as opposed to the electronics.
I'm thinking of the following design: bend a 20' steel 1" conduit into a circle. Then wrap say 16 gauge bare copper wire evenly and entirely around the doughnut creating a precision ring shaped electromagnet. Then power the ring shaped magnet with a variable DC supply to create the proper pull on, say, a 6lb steel pendulum that swings inside the ring. The idea is to adjust the voltage to give the electromagnet enough pull to keep the pendulum swinging, but not so much that it overcomes the force of gravity pulling the pendulum back to the center, thereby sticking the bob to the electromagnet. That solves the problem of keeping the pendulum moving.

ANSWER:
After thinking about this a bit, I believe there are serious
flaws here and your idea will not work. If you put a ferromagnetic material
(e.g ., your pendulum bob) in a uniform external magnetic field, that
field will polarize the material and essentially make it look like a bar
magnet with north and south poles. The south pole will feel a force opposite the
direction of the field and the north pole will experience the same magnitude
force in the direction of the field�a bar magnet in a uniform field
experiences zero net force (see left figure above). Admittedly, the field
due to your ring (see figure at the right above) is not uniform but, over
the size of your bob, it is approximately uniform. Forces due to the small
nonuniformity would be mainly in the vertical, not horizontal, direction.

QUESTION:
Hi I'm a high school student and having hard time understanding something about electric potential energy. Do electrons moving in a circuit have potential energy because battery has done some work moving them against electric field (from low potential to high potential)? If yes, suppose that I just put the wires around the battery and think about the moment when it took 1 electron from low potential to high potential. That electron now has a potential energy equal to the energy spent when moving the charge from low to high potential. But since a battery doesn't generate electrons (and just providing force to move them) and all other electrons were already there in the copper wire, how did other electrons get their potential energy? The battery hasn't done any work for them (or did it?).

ANSWER:
The electric current in a conducting wire is not the best way
to learn about potential energy of charges because it is a rather
complicate process. What happens is that the potential difference across
the ends of the wire cause there to be an electric field inside the
wire. Electrons see this field and therefore each believes that it is in
an approximately uniform field and therefore it accelerates and gains
kinetic energy as it loses potential energy it has by virtue of the
field. But what next happens is that little electron almost immediately
encounters an atom in the wire, collides with it, and loses some or all
the kinetic energy it has just acquired and has to start all over again.
So each electron bounces slowly along the wire, repeatedly gaining and
then losing kinetic energy. On average, there is a net drift of
electrons down the wire but it is really quite slow and we consider the
average electron to move with a constant drift velocity. So any
electron, moving from the negative terminal of the battery to the
positive terminal of the battery of potential difference V
moved, on average, with no change of kinetic energy but it has lost
eV
Joules of potential energy. Where did that energy go? Put your hand on
the wire and you will see that it has warmed up. If you want a more
lucid example of electrons and potential energy, imagine a uniform
electric field of strength E (like in the gap between plates of a
parallel plate capacitor) with an electron released at some point. Then
as the electron moves, accelerating along the direction opposite the
field (because it is a negative charge), it loses potential energy
eEz where z is the distance it has traveled. After it has
gone a distance z, it will have acquired a kinetic energy �mv ^{2} =eEz .

QUESTION:
As a chemistry teacher, I often get questions from students that are best asked of a physicist. Is there a "short" answer to explain the nature of charge? Why are there only two charges? We understand that the assignment of the negative to the electron could be completely arbitrary, but what exactly is a/the "negative charge"?

ANSWER:
For every force field in nature there is a corresponding
source of that field: gravitational mass is the source of gravitational
fields, electric charge is the source of electric fields, electric currents
are the source of magnetic fields, quarks are the source of nuclear fields,
etc . Further, if there are two such sources in proximity of each
other, each experiences a force due to the field of the other. We first are
aware of gravitational fields and conclude after some experimentation that
the property something must have to be a source of that field is mass.
Inspired by our success in understanding the gravitational field, we start
looking around for other forces. Combing our hair one morning, we notice a
new kind of force which is obviously not gravity. After some experimentation
we discover that some objects in nature cause electric fields if they have a
property which we call electric charge. So, putting two electric charges
near each other, we find, not unexpectedly, that both experience a force due
to the other. But now there is something different. In gravity, the force
between two masses is always attractive , never repulsive. So mass is
a relatively simple thing because there is only one kind of it. But with
electric charges, sometimes the force is attractive and sometimes repulsive,
so we conclude that there must be two kinds of electric charge which are
most easily distinguished from each other by assigning a sign, + or -. Of
course, further experimentation reveals that opposite charges attract and
like charges repel. Why are there two? Well, just because that is the way
nature is. You might just as well ask why there is only one kind of
gravitational mass. The way that quarks interact with each other is more
complex than just attractive or repulsive and three kinds of the quark
property called "color charge" are required. So the answer to "what exactly
is charge?" is that it is that property which something has which allows it
to both cause and feel an electric field.

QUESTION:
I know that simple generators produce electricity by moving a magnet through coiled copper wire. My question is does moving a magnet through a copper pipe also produce an electric current? Does it have to be coiled wire or will a copper pipe work too? I have seen the demonstration of lentz law of dropping a strong magnet through a copper pipe and how the magnetic field slows the drop rate but not sure if it also creates a small electrical current as well.

ANSWER:
That is the reason it drops slowly. Faraday's law says that if the
magnetic flux (strength of the magnetic field divided by the area it passes
through, sort of like pressure is force per unit area) changes, there will
be an induced EMF (like a voltage which can drive a current) which will
cause a current to flow around the circumference of the pipe. Lenz's law
says that the direction of this current will be such that its magnetic field
will oppose the change caused by the falling magnet. So, to the left you see
a magnet falling with its S pole down. So below this magnet a S-like field
is increasing and above it a N-like field is decreasing. So the current
below (above) creates a field which looks like a bar magnet with the S pole
up (down). Since like poles repel and opposite poles attract, both currents
try to keep the magnet from falling. Also, these currents are not so small;
they must be pretty big to have big enough fields to exert forces comparable
to the weight of the magnet. You would not likely feel them though since the
EMF forces the current through the copper, not you.

QUESTION:
in a charged conductor electric field inside it is zero but in a non
conducting charged object it is not so why

ANSWER:
The most important property of a conductor is that some of
the electrons in it are free to move. If you try to put an electric field
inside a conductor, the electrons will move and they will keep moving until
they exactly cancel out the original field. In a nonconducting material,
electrons cannot move and so if you put an electric field on it the
electrons may move a little but they cannot move enough to nullify the
original field.

QUESTION:
Why is the permittivity of free space not 1?

ANSWER:
Note that this constant has units, ε _{0} =8.8542x10^{-12}
C^{2} N^{-1} m^{-2} . The permittivity of free space
essentially quantifies the strength of electrostatic forces, F=q _{1} q_{2} /(4πε _{0} r ^{2} )
for the force between two point charges. But, if you redefine any of the
units�length, mass, time, charge�you will change the numerical value of ε _{0} .
For example, suppose you define the unit of charge as that charge which when
two 1 unit charges are separated by 1 m they exert a force of 1/(4π )
N on each other; call that unit of charge 1 Baker (B). Then ε _{0} =1.0
B^{2} N^{-1} m^{-2} .

QUESTION:
If two bulbs one of 60 watt and other of 100 watt are connected in series then 100 watt will glow more but I don't Know why?

ANSWER:
If the power rating of a bulb is P , this means that
P watts are consumed if a voltage of 120 volts is across it, so
P=IV=I ^{2} R=V ^{2} /R =120^{2} /R ,
so R =1.44x10^{4} /P . So, the resistance of each bulb is
R _{100} =144 Ω and R _{60} =240 Ω. When in
series, the same current passes through each and so the power is P=I ^{2} R .
It looks to me like the 60 watt bulb will be brighter because its resistance
is larger. For example, if the voltage were still 120 V, the current would
be I =120/(144+240)=0.313 A. The powers would then be P _{100} =(0.313)^{2} x144=14.1
W for the 100 watt bulb and P _{60} =(0.313)^{2} x240=23.4
W for the 60 watt bulb.

QUESTION:
If electrical currents are charged particles, then electricity must be composed of matter (obvious.....I think) if that were the case, then our thoughts, dreams, etc, are simply a result of charged neurons interacting within our synapses through electrical currents.
So, I suppose my question is, if our are thoughts are confined to ourselves or do they hold a place within the whole concept of time and space.

ANSWER:
Certainly, brain activity involves electric currents.
Electric currents create electromagnetic fields which can be detected
outside of you, so brain activity is not "confined to ourselves."
Neuroscience researchers routinely sense these fields with detectors outside
the subjects. If you are suggesting a possible explanation for ESP, I sure
would not bank on it. As far as we know, our brains are good at creating
very weak fields but not at detecting very weak fields. Also, there is
presently no known way of actually interpreting the thoughts which caused
those fields.

QUESTION:
I have a question concerning a magnet suspended inside a copper tube. Does the copper tube accumulate the mass of the magnet? In other words, does the copper tube now weigh more with the magnet suspended in the middle? or is it partial weight because the magnet does fall inside, albeit slowly.

ANSWER:
First, some terminology. Weight is the force which the earth
exerts on something, so the weight of the copper tube is always the weight
of the copper tube. If a magnet falls through a copper tube, it induces
currents in the copper and these currents exert a force on the magnet which
tends to slow it down. In fact, the force becomes strong enough that the
magnet quickly reaches a terminal velocity�it falls with a constant speed.
That means that the tube is exerting an upward force on the magnet equal to
the weight of the magnet. But, Newton's third law says that if the tube
exerts a force on the magnet, the magnet exerts an equal and opposite force
on the tube. Therefore, if the tube is standing on a scale, the scale will
read the weight of the tube plus the weight of the magnet, but that does not
mean that the tube got heavier. It is just the same as if you put the tube
on the scale and pushed down on it with a force equal the weight of the
magnet; you would not say that the tube got heavier because you pushed on
it. A good demonstration of this can be seen at
this link .

QUESTION:
Why do we divide by rsquare in coulomb's law and what is the role of 4pie in the constant of proportionality in the coulomb's law.
I am not able to understand as to why we divide the product of q1*q2 by 4 pie rsquare.

ANSWER:
The reasons for r ^{2} and 4π are
different. Coulomb's law is a statement of an experimental fact. If you have
two charges, q _{1} and q _{2} , and measure the
force F they exert on each other and then double either charge, the
new force will be twice as great; you have therefore found out
experimentally that F~q _{1} and F~q _{2}
(~ means "is proportional to"). Now, if you keep the charges constant and
double the distance between them you will find that the force gets 4 times
smaller; you have therefore found out experimentally that F~ 1/r ^{2} .
(Of course you would also do many other similar measurements like tripling
the charges or halving the distance etc .) Putting it all together,
Coulomb's law tells you that F~q _{1} q _{2} /r ^{2} .
But we usually prefer to work with equations rather than proportionalities,
so we introduce a proportionality constant k : F=kq _{1} q _{2} /r ^{2} .
The usual way to determine k is to measure F for a particular
q _{1} , q _{2} , and r . [Note that the SI
unit of charge, the Coulomb (C), is defined independently of Coulomb's law;
it is defined in terms of the unit of current, the Ampere (A), 1 C/s=1 A.]
You find that k =9x10^{9} N∙m^{2} /C^{2} .
Another way to put it is that you would find that two 1 C charges separated
by 1 m will exert a force of 9x10^{9} N on each other. That answers
your first question about why the 1/r ^{2 } appears in
Coulomb's law�it is simply an experimental fact, it is the way nature is.
Your second question is why do we often see the proportionality constant
written as k =1/(4πε _{0} ). There is nothing profound
here; later on when electromagnetic theory is developed further, choosing
this different form leads to more compact equations. Essentially, many
equations involve the area of a sphere which is 4πr ^{2 } which
means that there would be many factors of 4π floating around in your
equations of electromagnetism if you used k as the proportionality
constant.

Since I often think of
physical laws in terms of proportionalities, as I did above, I include here
another way this could have worked. Maybe you are content with the answer
above and can just ignore this! We could have used Coulomb's law to
define what a unit of charge is. Having done the experiment and
determined that F~q _{1} q _{2} /r ^{2} ,
we could have chosen the proportionality constant to be 1.0 if we wished to
define what a unit of charge is: F=q _{1} q _{2} /r ^{2} .
Now, 1 unit of charge would be that charge such that when two such charges
are separated by a distance of 1 m, the force each experiences is 1 N; that
new unit of charge would have been 1 kg^{1/2} ∙m^{3/2} /s=1.054x10^{-5}
C. In fact, if you do this in cgs units instead of SI units, where F
is measured in dynes (gm∙cm/s^{2} ) and r is measured in cm,
the unit of charge is called the statCoulomb (statC) and 1 statC=√(1 dyne∙cm^{2} )=√(1
gm∙cm^{3} /s^{2} )=1 gm^{1/2} ∙cm^{3/2} /s=3.34x10^{-10}
C. Personally, I think this is a more logical way to define electric charge,
but often history demands that we use the long standard definitions of
units; in the case of electric charge, the ampere, not the coulomb, is taken
as the fundamental unit.

QUESTION:
When a charged particle comes into existence from the decay of a neutral particle does the establishment of the associated electric field around the new particle constitute an electromagnetic wave? E.g when a neutron decays into a p, e and v I see nothing in the decay equation that includes the establishment of the p and e electric fields so am I right in thinking that the propagation of these new fields do not constitute electromagnetic waves?

ANSWER:
When a charged particle is created, an electric field is
simultaneously created. However, all space is not instantaneously filled
with that field but its existence propogates with the speed of light. So,
you will not know the particle is there until you can "see" it. Assuming
that the electron and proton move with approximately constant speeds after
the beta decay, there will be no electromagnetic radiation, just the
combined fields. They will also create magnetic fields because they are
moving.

QUESTION:
I have a question about fusion reactors. If the hot plasma in the reactor is contained in a magnetic bottle doesn't that shield us from receiving the heat to make power? How do we access the heat inside the magnetic bottle to use it to make power? What would happen if I tried to stick my hand into a magnetic bottle, would my hand penetrate?

ANSWER:
The magnetic bottle is just a magnetic field. You certainly
have no trouble moving your hand near a magnet where there is a magnetic
field. There is no reason why energy could not be transported out of the
magnetic bottle, it would just have to be carried by something with no
electric charge.

QUESTION:
So if you have a negatively charged iron ball (on the end of a plastic rod) and it exerts a strong attractive force on a penny even though the penny is neutral. How is that possible?

ANSWER:
The electrons in the penny are free to move because it is a
conductor. When the negatively charged ball comes close to it the electrons
on the side closest to the ball are repelled to the other side of the penny.
The side of the penny closest to the ball is positively charged and closer
to the the ball than the side which is negatively charged, so the penny experiences a net
attractive force toward the ball.

QUESTION:
I don't understand the reason why, when charged electrons are accelerated toward an equally charged positive plate with a hole through the center of the plate as in a simple two electrode cathode ray tube, why do the electrons keep moving past the positive plate? I would think that the electrons that pass through the hole should again be attracted to the positive plate and should slow down and reverse direction. What am I not understanding?

ANSWER:
The high voltage is applied across the cathode and the anode
so that there is a very strong electric field between them. But, beyond the
anode, the field is very weak. Think of a parallel plate capacitor where the
electric field outside the plates is zero.

QUESTION:
I read that the polarization of light is the direction of oscillation of its electric field. I also know that the magnitude of an electric field is given by the formula KQ/r^2 where K is Coloumb's constant, Q is the charge of the particle emitting the electric field and r is the distance from the particle. The fact that this formula has Q in it indicates that a particle needs a charge in order to have an electric field. Photons have no charge. Therefore, how does light have an electric field?

ANSWER:
Your statement "�the
magnitude of an electric field is given by the formula KQ /r ^{2} "^{
} is true only for the electric field of a single, stationary point
charge. However, electric fields in electromagnetic waves are certainly
generated by electric charges. But, for there to be a wave generated, rather
than just a static electric field, the charges must be accelerating. The
simplest example is the oscillating electric dipole, two equal and opposite
charges connected by a tiny spring so that they oscillate sinesoidally. The
animation to the right shows the resulting radiation from an oscillating
dipole (charges are oscillating vertically, the oscillator is too tiny to
see in this picture). The lines radiating out are loci of constant electric
field magnitude. The electric filed is perpendicular to the screen and the
magnetic field is perpendicular to the electric field and in the plane of
the screen. In nature, light usually comes from atoms which, if you think
about it, are composed of positive and negative charges and can therefore
look like a dipole when vibrating.

QUESTION:
It is my understanding that according to Einstein, magnetism doesn't actually exist, it is just a consequence of the relative motion of electric charges and the special theory of relativity. I have read explanations of how wires with electric currents flowing in them attract or repel each other due to nothing more than the moving electrons and their interaction with each other and the atoms of the wire via special relativity. But what about electromagnetic waves, where there is a varying electric and magnetic field? Can you provide a similar explanation that invokes special relativity and electric charges to explain electromagnetic waves?

ANSWER:
I would say that it is incorrect to say that "magnetism doesn't actually
exist." This gets a little complicated mathematically, but there is actually
only one field called the electromagnetic field. It is a tensor field, not a
simple vector field and when the Lorenz transformation acts on it, the
electric field and magnetic field (which are like "pieces" of the whole
field) both change. The simplest example is if you are at rest relative to
an electric charge there is only an electric field, but an observer moving
relative to you will see both a magnetic field and an electric field
(slightly different from yours). Just for the fun of it, I have written a
form of the tensor at the right. Notice that both electric and magnetic
fields are there, they "actually exist". You might want to look at the
Wikepedia article on the
electromagnetic field tensor .

QUESTION:
Will the force between two charges decrease if we place an infinite conducting plate between them?

ANSWER:
It depends on what the charges are. Qualitatively what
happens is that the electric field lines from both charges no longer
penetrate the sheet, so neither charge feels any force from the other
any more. However each charge now induces a charge on the surface nearest to
it and the net effect is like looking at a charge of the same magnitude and
opposite sign the same distance behind the sheet. So a charge of magnitude
Q and a distance d from the sheet will feel an attractive
force toward the sheet of magnitude kQ ^{2} /(4d ^{2} ).

QUESTION:
the speed of light is constant,yet we know gravity pulls on light,wouldn't light aimed directly towards a high source of gravity,such as a black hole move faster ?

ANSWER:
As light falls into a black hole, it gains energy, but not by
speeding up. The frequency increases as it falls meaning the energy of each
photon increases, but the speed stays just the same.

QUESTION:
I am a teacher in New Zealand, and am much more familiar with Chemistry than with Physics. I have been trying recently to understand magnetism better, in general, and as applied to Earth and Space Sciences. When a permanent magnet is created, what is actually lining up to create the magnetic field? I have heard it described as atoms, or pockets of charge, or micromagnets, but what does this chemically look like? Are they polar molecules within the solid? My understanding of bonding of metals doesn't include any polarity, they are positive nuclei in a 'sea of electrons', so how could a metal be aligned by charge? Is it an alteration of electron orbitals? Am I over-thinking this?

ANSWER:
An electron is, itself, like a tiny bar magnet, called an
electric dipole moment. In most materials, the electrons point in random
directions resulting in no bulk magnetism. In a ferromagnetic material like
iron, there is a quantum mechanical effect which causes the electrons
responsible for bonding to neighbors in the crystal to align their dipole
moments. An ordinary piece of iron is normally not a magnet because the
aligning of electron magnets happens only below a certain temperature called
the Curie temperature and when the iron cools down the alignment occurs
in local small volumes, each of which is pointing in a random direction;
these are called domains and are hugely bigger than atoms but still
microscopic. To magnetize the iron, you put it in a strong magnetic field
and the domains already aligned with the field will grow at the expense of
those not aligned with the field. You can also cool iron in a strong
magnetic field and then most domains will form being aligned with the
external field.

CONTINUED
QUESTION:
Also, how does the movement of charged particles in the Earth's liquid outer core, or in the Sun's convective zone, actually produce a magnetic field? I have read about this effect many times, but I just can't picture chemically what this would look like. Is it that the general movemnet of ions within a fluid tends to align in the same direction over time, thus influencing other ions to do the same, and this spreading the force?

ANSWER:
(In future, please follow site
groundrules and submit single
questions!) Any electric current causes a magnetic field. So a simple
model of the earth's field would be to imagine a huge ring of current inside
the earth. The magnetic field of a current ring is shown to the left.
Compare this to the field of the earth shown to the right. Clearly a model
where the core is thought of as a collection of current loops gives rise to
a reasonable description of the earth's field. You are barking up the wrong tree
by trying to understand it chemically. I should also note that the details
of the earth's field mechanism are not fully understood.

QUESTION:
i tried to find the time it would take for two charges to collide
under electrostatic force,realizing simple kinematics won't cut it,tired
to integrate but failed,how is the question done?and how does it differ
from gravitational force??

QUERY:
You have to define what "collide" means. Since it is a 1/r ^{2} force, if you use point charges the velocity will be infinite when they collide but they will do so in a finite time. Also, what are the initial conditions (velocities, positions), masses, charges.

REPLY:
My initial question was the time it would take for a 1/r^2,to
collide,for example two bodies lets say 1g,and a charge of 1micro
coluomb,initial at rest attract each other,and collide,I can't use
simple kinematics to solve this question,what shall I do?

QUERY:
How far apart are they?

REPLY:
ok,for simplicity 1m apart,is there a general formula than can help?

ANSWER:
Whew! I finally have everything I need. This is the Kepler
problem, the same, as you suggest, as the solar system with gravity. You
may want to look at an
earlier answer similar to yours. It is very lengthy to work out the
whole problem in detail so I will refer you to a very good
lecture-note document from MIT; I will just give you some of the
necessary results to calculate what you want. First, a brief overview of
two of Kepler's laws:

Kepler's laws refer to problems where the force
is of the form F =K /r ^{2} where K is
a constant and the force is attractive. So it could refer to either two
masses or two opposite charges.

The first law states that bound planets move in
ellipses with the sun at one focus. This is really only true if the sun
is infinitely massive but the generalization still leads to an elliptical orbit
for each body, both of which move around the center of mass of the two.
Still, the semimajor axis a of the ellipse (which we will later
need) in the center of mass system can be found for any orbit from the
simple equation a=-K /(2E ) where E is the energy of
the system.

For your case, the particles move in a straight
line toward each other and then turn around and return to their original
positions. This is just the most elongated possible ellipse with an
eccentricity of 1. Of course this would never really be possible in the
real world since the particles would be going an infinite speed when
they "collide". That means we really should do the problem
relativistically which would greatly complicate the problem. Keep in
mind that you are asking an unphysical question requiring point charges
and infinite forces and velocities. But the answer below should be a
good approximation of the time if they have some finite size small
compared to their initial separation.

The third law relates the period of the orbit
T to a : T ^{2} =4πμa ^{3} /K
where μ=m _{1} m _{2} /(m _{1} +m _{2} )
is the reduced mass. In the gravitational problem, K =Gm _{1} m _{2
} and in the electrostatic problem, K =k _{e} q _{1} q _{2
} where k _{e} =9x10^{9} N�m^{2} /C^{2} .

For your case, the energy is given since the charges
are initially at rest and separated by some distance S , so E =V (S )=k _{e} q _{1} q _{2} /S
and so a =k _{e} q _{1} q _{2} /(2k _{e} q _{1} q _{2} /S )=S /2=0.5
m; the reduced mass in your case is μ=m _{1} m _{2} /(m _{1} +m _{2} )=10^{-3} x10^{-3} /(2x10^{-3} )=0.5x10^{-3}
kg; and K =kq _{1} q _{2} =9x10^{9} x10^{-6} x10^{-6} =9x10^{-3}
N�m^{2} . Finally, the time it takes for a complete "orbit" (which
would correspond to the particles returning to their original positions)
would be T =√[4πμa ^{3} /K ]=√[4π (0.5x10^{-3} )(0.5)^{3} /9x10^{-3} ]=0.3
s. But, the time you want is just half a period, T /2=0.15 s.

To help you visualize the orbits, the figure below
shows the orbits for the two charges when the eccentricity is just less than
1; imagine the orbits getting flatter yet, approaching two straight lines.

NOTE
ADDED:
I got to wondering what the limits of doing this classically
are, that is, how good an approximation my calculation above would be for
some real system. This requires that I determine how close the two charges
would approach each other before their speed v became comparable to
the speed of light c . I will use the same notation as above and write
things classically. If released a distance S apart, then when they
reach a distance r apart energy conservation gives: k _{e} q _{1} q _{2} /S=k _{e} q _{1} q _{2} /r+ �μv ^{2
} which results in v =√[(2k _{e} |q _{1} q _{2} |/μ )(1/r -1/S )].
For the case in point, if I solve for r when v=c /10, a
reasonable upper limit for a classical calculation, I get r =4x10^{-8}
m, about 100 times bigger than an atom. Alternatively, we could ask what the
velocity would be for a 1 mm separation, r=S /1000: v =√[(2k _{e} |q _{1} q _{2} |/μ )(999/S )]=1.9x10^{5}
m/s=0.00063 c . In either case, I think we can conclude that the time
remaining to complete the half orbit will be extraordinarily small compared
to 0.15 s.

QUESTION:
One of Maxwell's equations is simply a correction to Ampere's law, which states that a magnetic field is induced by a current. Maxwell corrected this to say that a magnetic field can be induced by a both a current and a changing electric field (or more accurately, a changing electric flux).
Here is my concern. Since a current is a movement of electric charges wouldn't these moving charges create a changing electric flux? This electric flux would in turn induce a magnetic field, which becomes the equivalent of saying that the current induced the magnetic field. If the current and the changing electric flux are inducing the same magnetic field, it is in fact the same phenomenon, and Ampere's law doesn't need a correction. By this reasoning Maxwell's correction should instead be a generalization and would simply say that a magnetic field can only be induced by a changing electric flux (where in the case of moving charges the electric flux is caused by the current).

ANSWER:
Amp�re's law applies to magnetostatics, all current densities
being steady. And, if you think about currents in wires, there is no net
electric charge and so there is no electric field at all, so even if the
current is changing, there would (according to Amp�re's law) be no electric
field. You are apparently somewhat advanced to be asking this question, so I
put a more detailed explanation here , this being
primarily a site for layman questions.

QUESTION:
What is the difference between electric potential(infinity to a point) and potential difference(between two points)?
Why do we need two terms - electric potential and potential difference?
What's the use?

ANSWER:
Because of the definition of electric potential, it is always
arbitrary within an additive constant. Therefore, the only meaningful
quantity is the potential at one place relative to the potential at another,
so only potential difference is really of significance. For example, if you
call the potential at one place V _{1} and that at another
point V _{2} , you could just as well call the potentials V _{1} ' =
V _{1} +C and V _{2} ' = V _{2} +C
and there would be no change in any physics you do; note, though, that ΔV =ΔV'
because the C subtracts out. However, if you clearly state
where you have chosen the potential to be zero, then the potential
difference between that point and somewhere else is unambiguously
meaningful, and that is what is usually referred to as electric potential.
The electric potential at a point in space is simply the potential
difference between that point where you have chosen zero potential to be.
For example, for any localized charge distribution (not extending to
infinity), it is customary to choose V (r =∞)=0.

QUESTION:
If electric fields and magnetic fields both result from the same force (electromagnetic), then why do they interact differently with charged particles?

ANSWER:
Because the electromagnetic field is not a vector field, it
is a tensor field. OK, that is kind of technical, so let me try to clarify.
An electric charge at rest will interact differently with the x - and
y -components of an electric field (the E _{x} will
cause an acceleration in the x -direction, E _{y} in the
y -direction). The full field may be roughly thought of as having six
components and an electric charge will respond differently to all six. And,
they are all mixed up depending on your motion. If you have a pure electric
field but observe it from a frame moving by it, magnetic fields emerge like
magic.

QUESTION:
When you create an electric field or magnetic field is the field established everywhere in space the moment you activate the source? Or does the field build outward from the source?
example:
It is my understanding that when you turn on an electric magnet that the field it creates is created everywhere at once. So something x distance away that reacts to the field will feel it's effects as soon as the magnet is activated and something x + x distance away also feels the fields effects at the exact same moment.
If this is true have there been experiments to prove it and can you site any famous ones?

ANSWER:
An electromagnetic field propogates at the speed of light
through a vacuum. This is well known from electromagnetic theory which is
one of the best-understood theories of physics. Also, if an electric field
were to propogate instantaneously, you could send messages anywhere in the
universe instantaneously which is forbidden by laws of physics which are
known to forbid the transmission of information at a speed faster than the
speed of light. So, your understanding of an electromagnet is wrong. But it
might as well be right if you are doing an experiment in a laboratory where
the field appears very close to instantaneously across the room because the
speed of light is so large.

QUESTION:
Are electrons and protons respectively attracted preferentially to north or south magnetic fields-?

ANSWER:
There are many possible layers to this question:

You are probably just asking: "If I put an
electric charge near a magnet, what will happen?" The answer is nothing
because an electric charge only experiences a force in a magnetic field
if it is moving. Either a positive or a negative charge could be either
attracted or repelled from either a north or a south pole depending on
how it was moving.

However, electrons and protons are not just
charges but also have magnetic moments, that is, they are like tiny bar
magnets. So, treating them as infinitesimally small, they will
experience a torque in the magnetic field which will cause them to align
with the field so that the N (S) pole of the electron or proton will
point toward the S (N) pole of the bar magnet. Still, there will be no
force.

If we allow that the electron or proton magnetic
dipoles are not of zero size, then the nonuniformity of the fields (the
fields get weaker as you get farther away from the bar magnet) will
cause the proton or electron will be attracted to whichever pole it is
closest to.

QUESTION:
Why is it that when you place a metal sphere on a flat magnet, it will
spin real easily in one direction (i.e x-axis)? You can forceably spin
it in other directions, but along that single plane it just spins and
spins?

ANSWER:
The sphere becomes magnetized, so it looks approximately like
a bar magnet whose south pole sits on the north pole of the original magnet
(see figure at the right). To turn the ball about the x -axis requires
no torque but to turn it about the y -axis does require a torque.

QUESTION:
The Coulomb static force law represents the
electromagnetic force when a charge is at rest. When the charge is
moving, the magnetic force component is included (relativitstic effect).
The gravitational force law which is identical in form to Coulomb's Law
applies to mass. So is there a magnetic analogy for gravity when mass is
in motion? If so what is the term that is analogous to qv X B. Also
playing off this question... there are electric and magnetic constants
(permit, and permeab}... Why is gravity not treated this way (instead of
G, 1/4pi*constant) ... something like a gravity permittivity?

ANSWER:
The resemblance of the two force laws is not an indication that they are
in all ways similar. They are actually dissimilar in many ways:

gravity is nature's weakest force and electromagnetism very much
larger;
there are two kinds of electric charge, only one kind of mass;
the electromagnetic force is very well understood quantum
mechanically (with photons being the "communicator" of the force whereas
there is no theory of quantum gravity; and
gravity is understood in terms of the effect the presence of mass
has on the geometry of space, there is no electromagnetic analogy
to name a few. Regarding your second question, the factors of 1/4π
are for convience in electromagnetic theory to make some other equations
come out in simpler form; there is never any real physical significance to
how one chooses to write a proportionality constant.

QUESTION:
I've never received a clear answer on why they started
making household electrical appliance plugs polarized - that is one side
bigger than the other so the plug only goes into an outlet one way.
After all, AC is AC. I suspect it's a plot by under paid electricians.
Really, whats the deal?

ANSWER:
It is not a plot by electricians but rather a simple way of protecting
users from electrical hazzards. AC is not just AC; you need to have an
constantly changing potential difference across two wires but what is the
potential difference of either of these wires with respect to some other
potential we might define as zero? The zero reference potential is usually
simply the earth, that is we drive a steel stake into the ground and define
that potential to be zero. One of the two wires (called the neutral and the
one with the wider blade on a plug) is connected to the ground and the other
(called the hot wire and with the narrower blade) varies relative to the
neutral. Note that the neutral wire, even though it is always at zero
potential, will carry electric current and is therefore sometimes called the
return. If a switch is connected to a an outlet it is the hot wire which is
iterrupted to turn the outlet off so that you cannot get shocked if you
touch the outlet. Sometimes a third wire connects everything not electrical
(the outlet box, the metal box encasing your toaster, etc.) to ground so
that a malfunction of the device will not expose you to the hot wire.

QUESTION:
I'm trying to understand light wavelength, frequency and amplitude *physically* in addition to their depictions on graphs and in formulas. I got an A in high school physics years ago but felt then that I didn't really understand much as my head incessantly filled with questions as the class progressed. I spit the formulas back on demand on tests but had little confidence I actually understood what the heck was going on.
It recently occurred to me that depicting light as a wave drawn as a graph may have confused me. Such depictions seem to describe light as physically following a path just like the graph -- i.e., a graph's large amplitude represents an actual fat beam inside of which particles go up and down, defining the beam.
I recently started wondering if light wavelength, frequency and amplitude are really measurements of pulsating light particles' detectable energy, as if the light particles are glowing or even turning off and on, rather than descriptions of the shape of a light particle's physical path.
I. Do light amplitude, frequency and wavelength describe the following physical properties of light?
(A) is light AMPLITUDE the difference between pulses (glows; energy emissions?) of a light particle's dimmest and highest detected energy?
# if so, then amplitude does not describe the max height of an actual wavy physical path of light.
(B) is light FREQUENCY how fast a light particle pulsates (glows) from dimmest to brightest or off to on?
# frequency therefore does not describe the rate that a light particle travels up and down.
(C) is light WAVELENGTH the distance a light particle travels between one pulse ("glow")?
# wavelength therefore does not describe the length of a "strand" of a light wave between it furthest points from a straight line.
II. Is it possible to understand what the heck light is really PHYSICALLY doing without understanding advanced physics?

ANSWER:
You have numerous misconceptions here. I would recommend that you read
the Wikepedia article on
electromagnetic radiation . Let me give you just a
few basics. If you are unfamiliar with the concept of fields, then there is
no possibility that you can understand what light "is". However, if you got
an A in a physics course, there is a good chance that you understand what a
field is.

The picture to
the right shows what is "waving" in light. There are time varying
electric and magnetic fields as shown (the arrows in the sine-wave
shaped envelopes). This whole configuration moves to the right with a
speed c =3x10^{8} m/s. The relative magnitudes of the
electric and magnetic fields are fixed; they have been drawn to have
equal magnitudes here to make the picture easy to look at but they are,
in fact, not even measured in the same units so it does not really
matter what the relative magnitudes are in a picture like this. The
amplitude is simply a measure of how large the maximum electric field
is. The intensity of a wave of light, the rate at which it transmits
energy, is proportional to the square of the maximum electric field,
that is a wave with twice the amplitude will have four times the
brightness.
Also shown in
the picture is the wavelength of the wave (usually denoted as
λ )
which, you can see, is the distance between two successive maxima of the
electric field. The red end of the visible spectrum has longer
wavelengths and the violet end has shorter wavelengths.
Suppose you are
standing next to the wave as it is zipping past. Then the frequency
(usually denoted as f ) is the rate at which maxima of electric
field pass you. The frequency is measured in inverse seconds, for
example 500 maxima per second. The inverse second is often denoted as a
Hertz, 1 s^{-1} =1 Hz. Related to the frequency is the period
(usually denoted as T ) of the wave, the time it takes for one
wave to pass you. If you think about it for a bit you should realize
that the two are the reciprocals of each other, that is T =1/f.
Finally you
should realize that the frequency and wavelengths are not independent
since the wave moves with a specific speed c . The relation among the
three you can probably figure out by thinking sbout it a little: fλ=c.
Please note that your question violates the
site groundrule requiring "single, concise, well-focused questions". In
future questions please try to keep it more concise.

QUESTION:
The door of a domestic microwave oven is usually made up of a glass panel with wire mesh embedded in it. Why microwave couldn't go through the holes on the wired mesh? What physics phenomenon is involved. Is there any simple (or empirical) relationship between the shielding effectiveness of the wire mesh with the wavelength of microwave and the dimension of the holes on the mesh ?

ANSWER:
Shielding of electromagnetic waves can be effective if the grid spacing
is small compared to the wavelength of the waves. The wavelength of
microwaves is around 12 cm.

QUESTION:
Why does a magnegtic field moving in relation to any metal create an electric current, but the reverse is only true for a few metals. I realise that although I could explain in terms of some metals having domains etc. I don't really understand the relationship between electricity and magnetism - why do magnets cause a flow of charge, but a flow of charge only sometimes creates magnets?

ANSWER:
In fact, the laws of physics are perfectly symmetric: a changing
magnetic field causes an electric field and a changing electric field causes
a magnetic field. The first of these is called Faraday's law and the second
is part of Ampere's law. You seem to think that only a permanent magnet is
magnetism. In fact, any moving electric charge causes a magnetic field. The
most common source of magnetic fields is simply an electric current. Here
are some facts about electric and magnetic fields:

electric
charges cause electric fields,
electric
currents (moving charges) cause magnetic fields,
changing
magnetic fields cause electric fields, and
changing
electric fields cause magnetic fields.
QUESTION:
why electric filed lines do not intersect?

ANSWER:
Electric fields represent the force which would be felt by a unit
charge. If, at a particular point the electric field lines crossed that
would mean that the force on a charge would not have a single force on it,
so which one would it be? There might be two charges each of which had its
own electric field at some point, but the electric field at that
point would be the sum (vector sum) of the two; this is the superposition
principle.

QUESTION:
why does the TV cathode tube needs to be inside of a vacuum?
And can a light photon collide with an electron that is going from the cathode tube to the screen of the tv? If so, what type of scattering will that be? And will the electron still make it to the screen?

ANSWER:
Two reasons. First, the electron beam would collide with air on its way to
the screen and be lost. Second, very high voltages (kilovolts) are required
and would result in arcing if there were gas in the tube. A photon could
collide with an electron but energy and momentum considerations would cause
almost no effect on the electron's path. The scattering would be called
Compton scattering.

QUESTION:
Can a one turn coil using a large diameter piece of copper produce
the same magnetic field as a many turn coil made with thin wire? In
other words, what role does the gage of the wire play in the strength of
an induced magnetic field?

ANSWER:
What matters is the total amount of current which flows. 100 turns
carrying 1 ampere would produce the same field as 1 turn carrying 100
amperes. A thicker wire can carry more current than a thinner wire, so a
coil with a given number of turns of thick wire has the potential for a
higher field than for the same number of turns of thin wire.

QUESTION:
Why does light, if it is a result of the electromagnetic phenomenon
seem to exhibit little, to none of the properties of electricity or
magnetism (like charge for example)? I've asked about this before and
have been told that it's explained in Maxwell's field equations, but I'm
still in high school and won't be getting into that until university (I
think). Are you able to explain it without resorting to more advanced
mathematics like that?

ANSWER:
Everything about light and how it interacts is electromagnetic! When it
strikes your eye the electric fields in the light beam cause chemical
reactions and electrical nerve impulses in your eye. When a radio wave (the
same phenomenon as light, just not visible to our eyes) strike an antenna
the electric fields in the wave causes electrons in the antenna to move
around causing electric currents which can be amplified and decoded. All
electromagnetic waves are produced by electromagnetic phenomena, whether the
electrons in an atom jostling around or the electrons in your cell phone
antenna sending out messages. To understand, at least qualitatively,
Maxwell's discoveries is not really hard. It goes like this: there are four
fundamental equations which describe all aspects of electricity and
magnetism. These four equations, if manipulated mathematically, can be
transformed into two equations which are recognized by all physicists and
mathematicians as wave equations. The speed of the waves predicted by
Maxwell's equations just happens to be 3 x 10^{8} m/s, the speed of
light! Until this discovery, it was not known what light was but its speed
had been measured. If you want to read a little more detail about
electromagnetic waves, see one of my
earlier answers . You might also be interested in my earlier discussion
of
electric and magnetic fields
which is essentially Maxwell's equations in words.

QUESTION:
I'm a first year BSc student, and we have just covered electromagnetism. We were shown the formula for the speed of light in terms of the permeability and permittivity of free space, and how it showed that light is a self-propagating electromagnetic wave which abides by Maxwell's equations. Was this formula derived in any way, or was it found by fiddling around with the constants? If it was derived, where can I find the derivation? I know that the units conveniently cancel out to get m/s, and that it is quite aesthetically pleasing in the manner in which it unites electricity with magnetism, but understanding how this formula came about at a deeper level would really help me get a more rounded understanding of this fascinating subject.

ANSWER:
This is definitely the result of what could arguably be called one of
the most important derivations in the history of physics. In the latter half
of the 19^{th} century it was known that light was a wave but it was
unknown what was waving. Maxwell's triumph was, by taking his four equations
he was able to show that a solution was a wave which traveled with exactly
the speed 3x10^{8} m/s�some
coincidence, eh? If you are a first year student, you are probably not ready to
understand Maxwell's equations and the derivation since they involve both
vector calculus and partial second-order differential equations. In case you
are, I have attached an abbreviated derivation
(showing only electric fields); Maxwell's equations written here are for
empty space with no charges or currents. A little more detail can be found
here . You might also want to read a more qualitative explanation I gave
in an earlier answer and also to
read a little about
electromagnetic waves I wrote.

At the risk of
getting a little long-winded here, let me add that Maxwell's equations are
laws of physics and Einstein's principle philosophical belief was that all
laws of physics must be the same for all observers in the universe. Since
the speed of light is 1/√[μ_{0} ε_{0} ]
for the observer who wrote down Maxwell's equations here on earth, that must
be the speed for all observers. This is one of (unexpected) cornerstones of
the theory of special relativity. Again, see an
earlier answer .

QUESTION:
my question is regarding inductors i recently studied about inductors and i got really confused it was given that when a voltage is applied across an inductor an induced emf was generated which opposed the applied voltage also if the resistance of the coil and the wires was zero then the induced emf was exactly equal in magnitude to the applied voltage and thus the applied voltage and the induced emf were equal and opposite to each other .now if the two voltages are equal and opposite in magnitude their vector sum should be zero and no current should flow through the inductor however a current was shown flowing through the inductor i am really confused please help me

ANSWER:
The essential part which you are missing is that the induced emf depends
on the rate of change of the current through the inductor. So, if you just
hook it up to a battery there will be a constant current after a short time.
When you first attach the battery, current will start to flow and so there
will be an induced emf (but smaller than the emf of the battery) and as the
current gets bigger it will change more slowly until, eventually, a constant
current will flow. (The preceding assumes that the inductor itself has some
resistance or else a battery would cause infinite current to flow.) Now, if
you connect the inductor to an AC source the current will always be changing
and so there will always be an induced back emf which will impede but not
stop current flow. The higher the frequency of the AC source, the faster the
current will be changing, so the smaller the current through the inductor
will be.

QUESTION:
is the charge of a proton calculated to be exactly equal in magnitude with an electron? and what does it mean by saying equal magnitude?

ANSWER:
No, they are measured to be equal in magnitude to incredible
accuracy, no different than 10^{-13} %. Magnitude simply means that we discard
the signs of the charges, the electron charge is -e , the magnitude of
which is e .

QUESTION:
how does ac currrent move fromone place to another, if is goes back and front.

ANSWER:
It does not "move from one place to another".
For that matter, dc current almost does not either. The electrons move so slowly that it might take a day for electrons to move from
battery to light bulb. The important thing is that all the electrons in the wire are moving almost instantaneously when you close the switch,
ac or dc.

QUESTION:
for almost five years since we were taught, we've known that current is a scalar quantity having direction that does not obey vector laws, but, obeys Kirchoff's laws. However, I'm recently studying electrodynamics from Griffiths and it says that current is vector quantity. Its very confusing. If current is vector, it has magnitude and direction that obeys vector laws and also directions with respect to Kirchoff's laws. My feeling is that it is vector at microscopic scale and scalar at macroscopic scale. But, how come?

ANSWER:
Current density J is a vector. The current through
some area A is defined as _{A} ∫ J ∙ dA
over the area. So, current can be either positive or negative
depending on the sign of the dot product. It is not a vector, but its sign
matters, particularly when applying Kirchoff's laws as you have found.

QUESTION:
If you have a hollow copper sphere and connect the + terminal of a
battery to the copper ball, is the sphere considered to be charged? If
so, what is the charge on the sphere?

ANSWER:
You are raising the potential of the sphere to the voltage of the
battery. Assume the negative terminal is grounded so we can think of zero
potential at infinity. Then the potential will be V=kQ /R where
V is the battery voltage, Q the charge on the sphere (which
will be uniformly distributed on its surface), R the radius of the
sphere, and k =9x10^{9} Nm^{2} /C^{2} .
Therefore, Q=VR /k .

QUESTION:
Is there a metaphor or a simplistic explanation that I can use to
explain to middle schoolers that electricity and magnetism are
manifestations of the same force? Age-appropriate textbooks just state
that this is so without explanation, or else they simply give the
example of an electromagnet, which doesn't answer the deeper question.
Some books don't even explain that they are related! Introducing the
ideas of vectors and tensors makes the explanation too long and I lose
most kids' attention. Do you have any ideas?

ANSWER:
Sure, there are lots of ways to demonstrate the connection. Easiest
is to simply refer to an electromagnet. Here we have an electric current
going around a coil of wire and it will attract iron. You can easily make
one by wrapping wire around a nail and connecting it to a battery and show
that the nail becomes a magnet. Moving electric charges (which is what the
current in the wire is) cause a magnetic field. This connection was first
discovered by
Oersted , a Danish physicist of the 19^{th} century, who noticed
that, when he hooked up an electrical circuit, a nearby compass deflected
from north. You can demonstrate the connection also by changing a magnetic
field, for example by thrusting a magnet into a coil of wire. The changing
magnetic field causes an electric current to flow in the coil. Here is a
nice animation to demonstrate this. This is the basis of how electricity
generators work.

QUESTION:
I'm having difficulty conceptualizing the idea of electromagnetic waves (such as visible light) having a frequency and wavelength. I was sitting at my desk recently, sitting under a florescent light bulb which was flickering really fast, but slow enough for me to recognize it. I know that the light was blinking at a frequency of several times per second. Is this the "frequency" that physicist refer to when talking about the frequency of electromagnetic waves?

ANSWER:
First you should read an
earlier answer where I try to give some of
the basics of electromagnetic radiation. One important equation there is
f=c /λ where f
is the frequency, c the speed of light, and λ the
wavelength. Now, green light has a wavelength of about 555 nm=5.55x10^{-7}
m and the speed of light is about 3x10^{8} m/s. So, f =5.4x10^{14}
s^{-1} ; that is a whole lot bigger than several per second!

QUESTION:
i am inside a train,,the train is moving..and there is one electron inside a train ..and i am looking at that electron..in my perspective the electron is not moving and (as my high school teacher told) only moving charged particle creates magnetic field...so i will not see any magnetic field..but suppose my friend is looking that electron sitting outside the train..then he will see a magnetic field is created.because he will see that electron..then here is a problem...what is hapenning in reality..is there a magnetic field or not

ANSWER:
What you have discovered is that electric and magnetic fields
are not two different things. They sure look that way on first inspection
and the reason they are taught to be two different things is because of
history: it took a long time to find the connections between them. Two
centuries of experiments finally led to
Maxwell's equations , four
equations which show all the ways the electric and magnetic fields are
related. Maxwell's equations comprise a relativistically correct theory of
electromagnetism; it was actually questions like you ask which led Einstein
to discover the theory of special relativity. In its most sophisticated
form, we think not about electric and magnetic fields but the
electromagnetic field. The electromagnetic field is not a vector field,
rather a tensor field, and any field can be decomposed into its electric and
magnetic parts. Your friend on the ground will also see an electric field
but it will be slightly different from the field you see, which you may want
to interpret as some of the electric field transformed into magnetic field.

QUESTION:
Can you settle an argument raging between physics
teachers?
When a capacitor is charged by a battery in a series R-C circuit, how
much energy is 'lost' during the charging process?
Some say 'always 50%', some say 'less' and some say 'none'.

ANSWER:
At the end of the charging
process (technically infinite time, but for practical purposes much
greater than RC ), the voltage across the capacitor will equal V ,
the voltage of the battery, since no current is flowing. The energy
stored in the capacitor is therefore ½CV ^{2} .
During the charging process, the current through the resistor is given
by i =(V/R )e^{-(t/RC)} so the
instantaneous power loss in the resistor is i ^{2} R =(V ^{2} /R )e^{-(2t/RC)} .
If you integrate the power from t=0 to ∞ you will find the energy
lost to ohmic heating in the resistor is ½CV ^{2} .
So, exactly the same energy stored in the capacitor is dissipated in
the resistor. Hence, since the battery is the only energy source, half
the energy supplied is lost.

QUESTION:
How are electrostatic fields set up in space? I
believe I understand how to interpret such fields. What I am puzzled by
is how they originate or establish themselves, and how they are
maintained. Does the boundary of the field propagate at the speed of
light? Assuming it does, what is propagated? A wave? Or is it a pulse,
as in a 'nothing then something' pulse? Are there particles like
photons associated with this propagation?
For example, consider the field for a large charged flat sheet. It has
the same strength at any distance (less than say the smallest dimension
of the sheet), but it must set up some how? I'm puzzled by how. Then
once established, what is established? Does a electrostatic field
change a region of space for charges that find themselves in that
region of space? Also, the presence of a single charge will impact any
number of charges that enter the field (superposition), yet its effect
on any one charge is not diluted by the presence of others.

ANSWER:
Think of a crack starting
at one edge of a frozen lake and propogating across the lake. That is
essentially what electric and magnetic fields do but they propogate at
the speed of light. So, if you suddenly create an electric charge, the
field takes time to establish itself; so, if you were 300 m from where
the charge was created, you would not see a field from that charge for
3x10^{2 } m/3x10^{8 } m/s= 10^{-6} s=1 μs.
To answer the "…once established, what is established" question,
a field at some point in space will simply result in an electric charge
Q being placed there experiencing a force QE in
the direction of the vector E . Now, are they simple
mathematical constructs to help us visualize forces or, as you ask, do
they actually exist in the space where we visualize them? I believe
that the view that they are just a construct is wrong because an
electric field has an energy density, so energy resides where electric
or magnetic fields reside.

QUESTION:
In my high school physics class, we have just finnished the section on electricity. The two equations my question relates to are:
the relation between capacitance, voltage, and charge C=Q/V
the force between two point charges (Q and q) as a function of distance
F=(kQq)/d^2
My question, which none of my teachers can answer, is: Why don't these two eqations work when used together? I'm assuming they dont work because a capacitor of 100uF at 10v holds 1000uC and two charges of 500uC separated by 10cm should, according to those equations above, exert a force of roughly 225,000N. I've done the math many times and can't find any issues. Is it a calculation error or improper use of the equations?

ANSWER:
The reason is that the two equations are essentially unrelated. The force
equation applies to two point charges separated by a distance d .
The plates of a capacitor are not point charges. You also have some
misceptions about capacitors. The capacitor carries a charge Q .
This means that one plate of the capacitor carries a charge Q and
the other a charge -Q such that the total charge is zero. The
plates of a capacitor therefore exert an attractive force on each other.
It is pretty easy to compute the force one of the plates of a
parallel plate capacitor feels because the electric field between
the plates is nearly uniform. The field is given E =4π kQ /A
where A is the area of the plates, and the capacitance is
C=A /(4π kd ).
The force felt by each plate is F=EQ /2. If I put in your numbers
for Q =10^{-3} C, V =10 V, and d =0.1 m I find that F =0.5
N, a far more reasonable number!
QUESTION:
If a circuit has 12V and a bulb is attached it will glow twice as bright as the same bulb with 6V. From ohms law it says that for the 12V circuit twice as much current will flow. My question. Does the voltage make the electrons have more kinetic energy? and is this kinetic energy then transferred to the light bulb? If so does this mean in both circuits there are the same number of electrons but in the 12V circuit they are just faster?

ANSWER:
I will assume that the resistance of the
bulb stays constant. (It actually does not because as it gets hotter its
resistance changes; we'll ignore that.) Your very first statement is
false. If you double the voltage you will double the current. Since the
power (to which brightness is proportional) is the product of voltage
times current, the brightness will increase 4 fold. The number of
electrons participating in current flow is mainly independent of the
amount of current flowing, so, yes, more current means faster average
electron velocity. FOLLOWUP QUESTION:
You gave me an answer the other day about current and voltage which I really liked, and you showed me that the brightness of a bulb would increase 4 times (not 2) if voltage was doubled, thanks very much. I am working towards my theory papers for a 1st yr electrician and I just don't get how the energy from voltage is supplied to a load. Like, is it due to the kinetic energy of the electrons? Do the electrons always have the same charge (intrinsic electrical energy?) but are just moving quicker then release their energy in a collision with the load/resistance atoms, make heat/other energy? or do the electrons 'carry' extra charge? my teacher always talks about electrons as being like dump trucks. They have a little motor (the fundamental charge) then load up with extra energy and drop it off?

ANSWER:
A conducting material has approximately one
electron per atom which is essentially free to move around. Even if
there is no voltage, they are zipping around inside the material
randomly; the first approximation of a model of a conductor is to just
treat the electrons like a gas and it works pretty well. Now, when a
voltage is applied, there is an electric field set up inside the
material and the result is that each electron experiences a constant
force from the field. Now, if the electrons were truly free, they would
accelerate from the negative to the positive terminals. But they are, in
fact, in a material and they just get going and they hit an atom. This
collision essentially stops the electron and causes the atom to bounce
back a little, in other words the electron's acquired kinetic energy is
transferred to the atom. But, giving atoms in the material more energy
means increasing the temperature of the material. That is how the load
gets the energy from the current. Since you are studying to be an
electrician, I should perhaps mention here what I hinted at last time�the
light bulb changes its resistance as it heats up, that is it is not
truly an ohmic device. If you double the voltage, the current will not
double because the resistance does not stay the same as the bulb gets
hotter but increases.

QUESTION:
I am having a physics mental breakdown. My physics textbook (and experience studying physics) is contradicting popular belief and I would like to run this by an expert.
When it comes to magnets, opposites attract. North poles are attracted
to South poles and South poles are attracted to North poles. So when the
North pole on my compass points towards the Geographical North Pole,
that implies that the Geographical North Pole is really close to the
Magnetic South Pole, correct? Similarly, the South pole on my compass
pointing to the Earth's Geographical South Pole implies that the
Geographical South Pole is really close to the Magnetic North Pole.
Additionally, magnetic field lines are drawn from the North pole to the
South pole, so on the Earth they are drawn from (near) the Geographical
South Pole to (near) the Geographical North Pole. In summary, I have
been researching a few educational websites and most are saying
different (and contradicting) things. I believe that my physics book is
correct, but other physics sites have labeled the Magnetic North Pole
near the Geographical North Pole and the Magnetic South Pole near the
Geographical South Pole. Which is correct?

ANSWER:
This is not really worth having a breakdown about! The north pole of a
compass needle points in a generally northward direction. It is therefore
pointing toward a magnetic south pole. The geographic pole near the point
toward which a compass points is what everybody calls the north pole.
Geographers tend to call this point the magnetic north pole but, if examined
closely, magnetic field lines go into it, not out. It would be just too
confusing to everybody to call it the magnetic south pole. See the picture
at the right.
QUESTION:
my class and i were discussing since light waves are part of the electromagnetic spectrum as are radio waves, then could light waves be converted to sound just as radio waves are? a concert with ROYGBIV?

ANSWER:
When you listen to music on the radio, you are not listening to the
frequency of the radio waves. A trick called modulation allows one to use
radio waves (whose frequencies are far too large to be heard by the ear) to
carry a signal which has a frequency we can hear. The electronics in the
radio passes the sound frequency to its amplifier and speakers. Sound waves
which we can hear are in the range of about 20-20,000 cycles per second;
radio waves are in the range of about 0.5-100 million cycles per second. The
figure to the right shows an example of what is called amplitude modulation
(AM). There is also something called frequency modulation (FM) which is
similar but the modulating wave changes the frequency of the carrier instead
of its amplitude; it's a little trickier to visualize. You can modulate
light waves, but it is not as convenient and you could not use them for
long-distance transmission. But then, you wouldn't be "hearing red", for
example, but whatever you were modulating it with.
QUESTION:
What force confines electrons to a negatively charged metal? I've read
from many textbooks that a neutral metal confines its electrons because
as soon as an electron escapes into the vacuum it leaves behind a
positive charge that quickly attracts the electron back into the metal.
Thus the electrons are imprisoned inside the metal forever, unless a
high energy photon comes along to knock it out (or something of that
nature)... Well, what about metals (say a metal sphere sitting in
vacuum) that has a net negative charge?... It would seem to me that the
metal "wants" the electron to leave... What I mean is, as soon as the
electron leaves the metal it does not leave behind a positive charge
anymore (because the metal is charged negatively). It leaves behind a
negative charge that should push it away even further. What is the
mysterious force that is counterbalancing this repulsive force and
keeping the electron in?

ANSWER:
Imagine an electron very close to the surface of the sphere on the
outside. Its field repels electrons inside the conductor leaving a net
positive charge closer to the electron than the residual negative charge.
Hence, the electron outside experiences an attractive force.
QUESTION:
I'm trying to settle an office debate.
We are debating on how an electron travels through a conductor.
Lets assume we are taking about DC current through a copper wire.
I think that the electrons are passed from atom to atom on the last (4th) energy level.
Can you tell me if this is accurate, if not can you explain to some detail how it works?

ANSWER:
In a good conductor, the conduction electrons (those which, in an
isolated atom, would be called the valence electrons and are outermost) are
almost perfectly free to move around. The atoms behave differently in the
bulk than singly. In fact, a very good model of a conductor is simply that
the electrons move around freely like gas in a box. Now, when a potential
difference (voltage) is applied across the conductor, an electric field is
established which causes the electrons to experience a force in the opposite
direction from the field (since they are negative). If they were really
free, they would simply accelerate from one end to the other. However, as
soon as one electron starts speeding up along the field, it bumps into an
atom and stops, then accelerates again, etc., etc . The net effect is
for the conduction electrons to have, when all are averaged over, a net
drift velocity in the direction opposite the field direction. For normal
household currents this velocity is very small, smaller than 1 mm/s. It is
really not accurate to say the electrons "jump" from atom to atom; rather
the atoms and electrons suffer collisions.
QUESTION:
Light is considered as particle because of photoelectric effect. This is only one evidence. Are there any other experiments that shows light is made up of particles?

ANSWER:
Historically, there is an equally important experiment demonstrating
that light sometimes behaves like a particle�the
Compton effect. If electromagnetic radiation (x-rays were used in the
orginal experiment) their scattering from electrons can only be
explained with particles, not waves. Also, any time atoms or nuclei
deexcite, they emit single photons.

QUESTION:
Can I say the fact that light is able to travel through vacuum shows it consists of particles (since nothing is waving in a vacuum, so it make no sense that wave can exist in vacuum)?

ANSWER:
No, any electromagnetic radiation can be either a particle or a wave
in vacuum, you find what you look for. This is called wave-particle
duality. A wave can travel through a vacuum because what is "waving" are
electric and magnetic fields which can exist just fine in a vacuum.

QUESTION:
In a standard textbook example, a charged particle moving with a constant moderate velocity perpendicular to a constant magnetic field is deflected.
If an uncharged observer is traveling parallel to the charged particle with the same velocity, it would see the charged particle as having zero velocity at first and then motion in the direction of the deflection observed by the stationary observer.
If the magnetic field is "constant", how does the co-moving observer explain the force on the charged particle?
I guess another way to ask the question is if charged particle motion in a magnetic field produces a force on the particle, and motion is relative (to the field), then is it possible to have "moving" field produce a force on a "stationary" particle?
Or more fundamentally yet, if the field is constant, how does the particle "know" it's moving through the field?

ANSWER:
What a good question. The thing is that electric and magnetic fields are
not really different fields like all elementary texts make it look.
There is one field, the electromagnetic field and the "mixture" of how
much of each is electric or magnetic depends on the frame of reference
of the observer. If, in a particular frame of reference, there is a pure
electric field, then if you view this field from a moving frame, a
magnetic field will appear. Similarly, if, in a particular frame of
reference, there is a pure magnetic field, then if you view this field
from a moving frame, an electric field will appear. The situation you
describe is the second and it is then the electric field which produces
the force on the particle "at rest".

QUESTION:
I came up with a thought experiment described below.
I setup a potential difference of say V volts between two horizontal parallel plates kept fixeda certain distance apart.I have given the upper plate +q C charge & the lower plate -q C charge.This system of course has some energy that depends on the charge in the plates and the plates separation. Now what i do is I pass a negatively charges particle with some initial kinetic energy, say Ei and velocity component purely horizontal , halfway through the two plates . As the particle emerges out of the electric field, it has gained some velocity along the vertical direction and thus has a kinetic energy Ef, greater than Ei. The difference dE = Ef - Ei is obviously positive implying it has apparently absorbed some energy from the field in course of its passage through it. As far as I believe, this brings about no change in magnitude of charge in either of the plates and the separation between plates has been held constant. So in no way is there a change in the energy of the parallel plates system.
It follows that by doing this I have managed my little particle to gain some energy without any other system having lost it!!

ANSWER:
Ah, the seemingly simplest questions are often the hardest for me to
come to grips with! Here, as has happened before, we have a situation
where we apply ideas about idealized simple situations and end up in
trouble. We assume that the parallel plates were charged up in complete
isolation from the rest of the universe. Further we assume that nothing
will disturb these plates, their charge distributions or positions, no
matter what we do. So, suppose that there is, in all the universe, only
two plates, one point charge, and a battery. The battery charges the
plates and the work it does is stored in the electric field which
appears; then it is removed from the universe. When we calculate the
energy necessary to charge the plates, we do it just the way our
physics teachers told us to do it. But, wait a minute�our
teachers never told us to worry about the field caused by our particle
we are about to shoot through, but does that not make a difference? If
there is some other field present the work to charge the plates will be
different from the ideal case. In essence, the particle has a potential
energy by virtue of its position vertically and this was imparted to it
when the plates were charged by the battery. (A colleague pointed out to
me that this problem is really no different from asking where the energy
comes from when I drop a stone.) Also, when the particle passes through,
the charges on the plates and the plates themselves will be pushed
around. But, the energy which "magically appears" is normally
infinetesmal compared to the total energy stored in the (not really)
uniform and constant electric field. So, once again, the physics we
learn in a physics class is only an excellent approximation to what goes
on in the real world. My argument would be that the electron already had
the energy it appears to acquire, but in the form of potential energy it
acquired when the field was created.

QUESTION:
Does the frame of reference concept carry over into the interaction between electrons and magnetic fields? Specifically, does a magnetic field only result from an electron moving relative to an observer? For example, would an observer not moving relative to an electron not see a magnetic field and an observer moving relative to an electron see a magnetic field?

ANSWER:
If the electron were a charge alone, it does not have a magnetic field
if at rest. However, since the electron has a magnetic moment (i.e. it
looks like a tiny bar magnet), it does have a magnetic field when at
rest. If it is moving, there is an additional magnetic field due to the
moving charge.

QUESTION:
I'm trying to understand Maxwell's but I can't!
There is a lot of maths and I'm still 15 which means I'm not ready for that kind of level!
But how can I be a physicist without understanding Maxwell's ? Could you please explain it to me sir?

ANSWER:
Since you cannot do the mathematics, I can only give you a brief
qualitative explanation of what Maxwell's four equations say. Maxwell's
equations tell you everything there is to know about electricity and
magnetism. They also contain the theory of special relativity; they
predict the speed of light and demonstrate that light is nothing more
than varying electric and magnetic fields. You need to know what an
electric field and a magnetic field are: electric fields, when present,
cause an electric charge to feel a force and magnetic fields cause a
moving electric field to feel a force. Here are Maxwell's equations:

Electric charges cause electric fields; a
point charge causes a field which falls off like 1/r ^{2} ,
r being the distance from the charge.

Electric currents (moving charges) cause
magnetic fields.

Changing electric fields cause magnetic
fields.

Changing magnetic fields cause electric
fields.

That is about what you can do without math.

QUESTION:
why do the electric line of forces pass through an insulator but not a conductor?

ANSWER:
The definition of a conductor is that the electrons are perfectly free to
move around inside. Therefore if there were an electric field inside the
conductor, the electrons would be accelerating because of the force they
feel. All electrons, for a static field, end up on the surface and
create a field of their own which exactly cancels out the applied field.
It should be noted that an electric field can exist inside a conductor
if it is changing with time, you just cannot have a constant electric
field inside.

QUESTION:
when a highly charged metal cube is placed in vacuum, will it
exhibit corona dischargs???

ANSWER:
Corona discharge normally refers to the glow around the area of
discharge. In a gas, either a positively-charged or negatively-charged
object can exhibit corona discharge; the two are quite different
mechanisms�see the
Wikepedia
article . This, of course, would not occur in a vacuum since it is the gas atoms
which glow. In a vacuum, if the object is negatively charged, electrons
can leak off if the charge gets big enough; you could call this
"discharge" without the corona, I guess.
Any time the electric field at the surface of a negatively charged
object is large enough to remove an electron from the surface, electron discharge will occur. So,
if the charge is
large enough it will "leak" off. You are wanting a more quantitative
answer, though. A cube is a very hard shape to do an analytical solution for. I can only give you a qualitative overview of the problem. When you add electrons they will arrange themselves on the surface in such a way so that the electric field inside the cube is zero. The surface charge density will be largest near the corners. Even if the charge density were uniform, the field outside the cube would be largest at the corners, so you can be sure that, as you add charge,
discharge will occur first at the corners of the cube. Discharge will begin when the electric field at the surface is large
enough to remove an electron from the surface. I suspect that there is no analytical solution to this problem; you would probably have to do a numerical calculation on a computer. Note that the crucial quantity for discharge is the surface charge density, so the answer to your question depends on the size of the cube; the quantity you should seek is (total charge)/(area of cube).

In a vacuum there is no discharge if the net charge on the cube is
positive. In a gas, the cube will capture electrons from the gas to
reduce the positive charge, but that cannot happen in a vacuum, of
course.

QUESTION:
two permanent magnets will repel each other indefinitely
often with great force
not hard to make a permanently magnetically levitated platform
Where does the energy to perform the work come from?

ANSWER: One of the
truths of electromagnetism is that a magnetic field never does work, you
never get work (create energy) directly from a magnetic field. The simple
reason is that the force of magnetism on a moving charge is always
perpendicular to the charge's velocity. The explanation is always that an
induced electric field is what actually does the work. The case of permanent
magnets is more complicated than most to try to explain explicitly, so I
will give a similar example, taken from the classic text Introduction to
Electrodynamics , David Griffiths, Prentice Hall Publishers. In the
figure to the right there is a constant current in the loop as
indicated and there is a magnetic field pointing into the page in the
cross-hatched area. The upward force on the loop is just right so that the
weight, mg , levitates. Of course, right now, no work is being done
since the force is not moving the mass. But, suppose that the field is now
increased so the upward force now exceeds mg . Now the mass starts
rising. The magnetic force is doing the work, right? Wrong! Before you
increased the field the direction of the electrons' velocity was to the left
(don't forget the electrons go in the direction opposite the current). But,
when the loop starts moving up, the electrons now also have a component of
their velocity upward and that gives rise to a component of the force on the
electrons which is to the right; but this would reduce the current which we
have stipulated to be constant. So the battery in the circuit (which is not
shown but has to be there if there is a steady current) has to supply more
energy than before and that is where the work done on the rising coil comes
from�the battery. This is really just
Faraday's law, an induced back EMF in the loop arises because of the
changing flux. I know this is not the exact question you asked, but, trust
me, all "where does the energy come from when magnetic fields seem to
do work " questions boil down to similar explanations�an electric
field you forgot to think about.

QUESTION:
how does the electric force changes into magnetic force by giving certain velocity to the observer i.e. how are these 2 forces frame dependent?

ANSWER: Actually,
electric and magnetic fields are not different things, they are
manifestations of a single field, the electromagnetic field. When you
transform from one frame of reference to some other moving frame, you change
the mixture of the electric and magnetic parts of those fields. For example,
a point charge at rest has a pure electric field; but if you view it from a
moving frame of reference, it has both an electric and magnetic field. It is
far too involved to show the details here. The reason that we still talk
about electric and magnetic fields in elementary physics courses is that,
historically, it took a long time to realize their connections. The
electromagnetic field is not a vector field, it is a tensor field, a field
which has more than 3 components.

QUESTION:
an electron moving perpendicular to a magnetic field experiences lorentz force , here there is action but where's the "equal and opposite" reaction force . Is the newton's third law of motion being violated here.

ANSWER:
The field is being produced by a current somewhere and the "reaction
force" will be on that wire. However, that force is not necessarily equal
and opposite to the force on the electron. Newton's third law, as taught in
elementary physics, is not really absolutely true and magnetic forces, since
they are velocity dependent, are the best example to show this. The figure
shows two positive charges moving with velocities shown by black vectors.
The electrostatic forces are red and are equal and opposite. The magnetic
force felt by the particle moving horizontally is zero because the field
there (due to the other charge) is zero. The field due to the charge moving
horizonatlly points up out of the screen, so the magnetic force (blue) on
the other charge is to the right. The net force on each particle is shown in
green and they are neither equal nor opposite. Newtonian mechanics takes on
new forms in electromagnetism and everything still all hangs together,
but you need to include the energy and momentum densities of the fields.
This is way beyond the scope of this site to address.

QUESTION:
All the diagrams of electromagnetic waves that I have seen in textbooks show the electric and magnetic waves being 180 degrees out of phase. I always thought that the decay of one field caused a buildup of the other and that this would put them 90 degrees out of phase. Are the pictures wrong?

ANSWER:
I do not understand what you mean by phase. In the figure to the right
the electric and magnetic fields are in phase ; this is the diagram
you normally see. The fields are in phase in a vacuum or a nonconducting
medium. In a conducting medium they are not in phase, but I do not think
that is what you are interested in. This phase relationship is what is
predicted by solving Maxwell's equations. What is shown here is what is
called a sinesoidal plane-polarized plane wave; the wave fronts are infinite
planes, the electric fields are everywhere along one dimension and the
magnetic fields are everywhere along one dimension perpendicular to the
direction of the electric fields.

QUESTION:
I thought that magnetic and electric field lines were just convenient representations of how fields varied around charges and magnets, and, in reality the electric field, for example, would vary continously with distance. If this is the case, why do we see lines around bar magnets when sprinkled with ion filings, or lines between parallel plates in castor oil when sprinkled with semolina? What happens between the lines?

ANSWER:
You are right, the lines are just what we draw to convey what the field
is like, there aren't really lines. Let me talk just about the iron filings
around a magnet since both cases have a similar explanation (polarization).
Focus your attention on an iron filing: it becomes polarized, that is it
becomes a tiny magnet and it aligns itself with the magnetic field of
wherever it is. Now, look at its neighbors: those near its ends will also
be polarized but their N(S) pole will be close to the S(N) of our first
filing, and they like that; but those alongside it will have their N(S)
poles close to the N(S) poles of our first filing and will tend to be pushed
away. The net result will be chains of filings separated from each other.

QUESTION :
I teach 5th grade science, and I desperately need a fifth grade answer
to this question. I have wonderful bright students who ask excellent
questions and I stuggle to answer accurately without completely
overwhelming them.
"If light is electromagnetic waves caused by the vibrations of atoms or
electrons, and if a vacuum is defined as the absence of all matter;
then how can light travel in a vacuum?"

ANSWER:
Imagine two magnets in a vacuum. Do
they exert forces on each other? The answer is yes as you could prove
in your classroom if you have a bell jar to create a vacuum in. What
about electric forces? Think about an atom: the nucleus exerts a force
on the electrons even though there is a vacuum between the nucleus and
electrons. So, both electric and magnetic forces can be transmitted
through a vacuum. Physicists often express the presence of forces
experienced at some point in space by the existence of something we
call a field. If a magnet feels a force it is because it is in a
magnetic field; if an electric charge experiences a force, it is
because it is in an electric field. Hence, fields can exist in a
vacuum. An electromagnetic (EM) wave (like light, radio waves,
microwaves, x-rays, etc .) is composed of electric and magnetic
fields which are oscillating and move through space with a speed of
186,000 miles/second. A picture of an EM wave is shown above. Think of
this as a snapshot; a little later the whole thing will have moved to
the right. This is why EM waves have no trouble propogating through a
vacuum.

Extra material for the teacher if you think the kids can
get it:
If there are fields in a wave, then where are the charges and magnets
which cause fields? It turns out that if a magnetic field changes it
can cause an electric field (which is how generators work) and if an
electric field changes it can cause a magnetic field (which is how
electromagnets work). Therefore, if you get a wave going (from an atom
or from an antenna), it will keep itself going as it propogates.

QUESTION:
Hello, I'm a high school student and I have a few
questions which are probably very annoying. For most of these things I
have only been able to get circular or abstract meanings which don't
explain HOW and WHY these things occur. Here's one of them:
1) What is charge actually? (not just when it's said that an atom is
charged because it has more positive/negative protons/neutrons etc.,
but also the charge that forms electric fields. In other words what
exactly are coulombs measuring, and what DOES and electric current
consist of?).
Thankyou!

ANSWER:
The problem often is that people don't know what physics
is. In many instances, particularly at the foundations, we are
compelled to be empirical, to simply acknowledge that some things are
because they are. We begin doing physics by looking around at forces in
nature. We feel our own weight, the force the earth exerts on us
because we have mass and, through many experiments and calculations, we
discover that two objects that have mass exert forces on each other.
But we don't really know what mass is, do we? It is a property that
most things in the universe have which allows them to exert and feel
gravitational forces. That may be unsatisfying to you, but sometimes it
is the best science can do. Armed with our experience studying gravity,
maybe we now look around for other kinds of forces in nature. One day
when combing our hair we notice that there seems to be a mysterious
force which attracts our hair to the comb, seemingly having nothing to
do with gravity. We start doing experiments and make a remarkable
discovery—some objects in the universe possess a new property which we
decide to call electric charge which allows them to cause and feel this
new force which we call the electromagnetic interaction. It is a force
much stronger than gravity and may be either attractive like gravity
always is or repulsive; hence we conclude that there are two different
kinds of charge whereas there is only one kind of mass. But what
actually is charge? We really don't know, we simply infer its existence
by observing nature.

QUESTION:
Some 30 years ago I took an electronics course and there
was an ongoing debate over the amount of time it took from when power
was first applied to a circuit to when it was available throughout the
circuit. Some said it was instantaneous, while others argued the point.
I was never fully sure if what they really meant was "relatively
instantaneous" (as in the speed of light), because for all practical
purposes there would be no effective difference in most circuits. Do
you have an answer?

ANSWER:
Hell, I have an answer for anything; I might not be right
though, my wife tells me. When you switch on a light it comes on
instantaneously. Or, does it? As you probably know, the drift speed of
the electrons which flow in the circuit are very small, much smaller
than a millimeter per second. However, that which moves the electrons
is an electric field in the wire and when you turn on the switch, the
field appears in the wire at the speed of light, so it is not really
instantaneous, but since the speed is so large, it is for most
practical purposes. There are other effects which make more noticible
delays. When a current starts flowing in a loop, a magnetic field
starts building up and this changing field causes a back emf around the
circuit which opposes the increase of current; this is Lenz's law.
Another way of saying this is that the self inductance of the circuit
will keep the current from changing too fast. So if you had a simple
circuit with a resistor, a battery, and a switch and you watched the
voltage across the resistor with an oscilloscope when you closed the
switch, you would see a time much longer than the speed-of-light time.

QUESTION:
If there is a magnetic bar with a strong magnetic field pointing from the floor to the ceiling. am I correct that if protons, neutrons and electrons are brought near it the protons will be least effected?

ANSWER:
You have to be careful to specify how the particles are moving. If they
are at rest or moving in the direction of (or opposite) the field, then the
neutron will experience zero Lorentz force because it has zero charge. Let's
simply ask about putting each at rest in a uniform magnetic field. None will
experience a force but all will experience a torque because each has a
magnetic moment, that is, each looks like a tiny bar magnet. The electron
has, by far, the biggest magnetic moment and will therefore experience the
biggest torque; the proton has a magnetic moment larger than the neutron's
and so it will experience a larger torque than the neutron. If you put them
in a nonuniform field (which would be the case for the bar magnet you
specify), each will feel a force in proportion to its magnetic moment, so
again, the electron would feel the strongest force and the neutron the
weakest.

QUESTION:
I have a question about Einstein�s paper on The Special Theory of Relative (STR). In the introduction there are some references to phenomena that I have never heard of. Are there differences with what happens when moving the magnet verses moving the conductor? Is there a phenomenon where there is a difference in the electrical field around the magnet and a difference with an electromotive force without a corresponding energy? Or is Einstein saying that the customary view (I assume the Maxwell�s view) is wrong and that what is observable is the same for moving a conductor or moving the magnet?

ANSWER:
I believe that it was well known that it does not matter whether you
move a coil toward a magnet or a magnet toward a coil, in either case an EMF
around the coil will occur. But, it was puzzling because in the first case
the electrons in the wire are moving through a magnetic field and therefore
experiencing a force which propelled them around the coil and, if the coil
was open, caused a voltage across the ends; in the second case, there was no
apparent law of physics which said that if the field moves and the charges
stand still the charges will experience the same force as if it wer them
which were moving. Relativity takes care of this because there is no
preferred frame of reference and the two should be identical.

QUESTION:
When light is "slowed down"
because it enters a different medium what exactly is happening? How is
lights velocity rduced throught water or glass? Why does this
refraction happen?

ANSWER:
The answer is a little lengthy, so bear with
me. There are two important constants in electromagnetism (EM) which
essentially specify how strong the electric and magnetic forces are in
a vacuum; these are e _{0} (electric constant, called the
permitivity of free space) and m _{0} (magnetic constant, called the
permeability of free space). It turns out that when you do the
mathematics you find that the EM equations (called Maxwell's equations)
predict waves which have a speed of [e _{0} m _{0} ]^{-1/2} and this speed
just happens to be the speed of light in a vacuum. However, things are
different in a material: because the material is composed of many
charges and the charges are moving, the whole medium is affected if
exposed to electric or magnetic fields. For example, an electric field
will polarize the molecules and this polarization will result in a
weaker electric field than if the material were not there. Hence the
strength of the forces are different so we need to measure new values
of permitivity (e ) and permeability ( m ) both of which are
larger than the free space values. So now Maxwell's equations predict a
new (smaller) velocity [ em ]^{-1/2} . In a nutshell, the speed
changes because of the interactions of the electric and magnetic fields
of the light with the electric charges and currents inside the material.

QUESTION:
I made this question up
myself when pondering how to teach Newton's 3rd law:
A pulse of electricity through a wire produces an electromagnetic field
that travels outward at the speed of light. This field encounters a
charge and exerts the appropriate forces on it. While the forces are
occuring on the charge, on what is the reactionary 3rd law force? I
believe that the closed loop nature of the fields would render the net
work done as zero.

ANSWER:
Here is a dirty little secret we never
reveal to our students in introductory physics: Newton's third law is
not always true! Particularly in electrodynamics, it is rather easy to
see in simple examples. The culprit, as you seem to have intuited, is
the magnetic forces. As a simple example suppose you have a particle
(#1) of charge q moving in the positive x- direction
with speed v along the positive x -axis and a particle
(#2) of charge q moving in the positive y direction
with speed v along the positive y -axis. Particle 1 sees
a magnetic field pointing in the negative z-direction due to particle 2
so it experiences a force in the positive y -direction; particle
2 sees a magnetic field pointing in the positive z-direction due to
particle 1 so it experiences a force in the positive x -direction.
Of course, each particle also experiences a repulsive electrostatic
force but these do obey Newton's third law. But the net force does not.
If the magnetic forces involved were due to magnetostatic forces, long
steady currents, Newton's third law would be obeyed (as in the well
known force between two long parallel current carrying wires on which
the definition of the Ampere is based). It turns out that for the
electromagnetic field, one must include energy and momentum densities
of the fields themselves to do Newtonian mechanics and then all is
well. If you want to pursue this further, I would recommend the
intermediate-level E&M book by Griffiths.

QUESTION:
V=IR
Either increase R or I Voltage(V) will increase
Which of the two we are increasing in a step up transformer while
increasing the voltage as far as I know Current (I) decreases while
stepping up the voltage than is it the R that we are increasing?

ANSWER:
A transformer is not an "Ohmic device" and
so Ohm's law is not true. The reason that I decreases when the
voltage increases is that energy must be conserved and the power, the
rate at which energy is consumed (or delivered) is P=IV . So P _{input} =P _{output.}

QUESTION:
What is the shortest
wavelength (I assume in the gamma range) that has ever been
experimentally observed.

ANSWER:
The most energetic photon which I could find
reference to was a cosmic ray of energy 3.2 x 10^{20} eV
(observed in 2004 by the Fly's Eye Detector). Since E=hf and f=c/ l , l =ch/E= (3
x 10^{8} m/s)(4.1 x 10^{-15} eV s)/(3.2 x 10^{20}
eV)=3.8 x 10^{-27 } m. Here, h is Planck's constant and
c is the speed of light

QUESTION:
I am fascinated by
magnetism, most likely because I do not understand its limits. I
recently read somewhere that it has been determined that gravity
"flows" at the speed of light (i.e. if the sun were to inexplicably
vanish, it would still take eight minutes for it to disappear from the
sky and for the earth to drift from it's orbit). Does a magnetic field
behave similarly, or is it instantaneous in effect?

ANSWER:
Electromagnetic fields all
propogate at the speed of light. Thus, if you created a magnet on the
sun, it would take 8 minutes before you saw the magnetic field on the
earth.

QUESTION:
Why is the speed of light given by 1/sqrt(permittivity
*permeabillity)? What is the great mistery behind such a simple
relation?
How these two parameters combine to give the speed of light?
Why does the vacuum (nothing...) has physical properties such as
permittivity and permeability?

ANSWER:
This is the great triumph of Maxwell's work
in the 19^{th} century. There are laws of electromagnetism
which can be summarized in four equations, now known collectively as
Maxwell's equations. The quantity e _{0}
(permittivity of free space) is just a proportionality constant which
tells you how strong the electric force is and, of course, it appears
in the equations. Similarly, the quantity m _{0}
(permeability of free space) is just a proportionality constant which
tells you how strong the magnetic force is and, of course, it appears
in the equations. (In this context, there is nothing wrong with empty
space having permittivity and permeability because one certainly does
not need matter between charges or currents for them to exert forces on
each other.) When Maxwell messed around with the equations he
discovered that they could be rewritten as wave equations and that the
speed of these waves had to be 1/[e _{0} m _{0} ]^{1/2} . That this happened
to be the speed of light was the point in the history of physics that
we understood what was doing the waving in light waves--electric and
magnetic fields.

QUESTION:
Why are electons considered
negative? Is there anything that makes them specificly negative or is
that just the charge that scientists assigned it?

ANSWER:
There is no good reason. All the mathematics
of electricity and magnetism would be just the same if we called
electrons positive. The important thing is that there are two kinds of
electric charge (unlike gravitational mass for which there is
apparently only one kind) and it is convenient to label one positive
and one negative. The convenience is in the mathematics; e.g .,
if the force between two positive charges is repulsive, then so is the
force between two negative charges because the force depends on the
product of the charges. By the same token, the force between a positive
and a negative charge will be attractive. Incidentally, it was Benjamin
Franklin who originally labelled the the kind of charge which electrons
happen to be as negative (electrons had not been observed individually
in his day).

QUESTION:
Is electricity just
magnetism at rest? Why do we treat electromagnetism as two separate
vectors?

ANSWER:
You might say that magnetism
is what happens when you put electricity in motion. You are right that
we should not treat electricity and magnetism as two different things
since they are really both parts of electromagnetism. We treat them
separately for two reasons. First, this was the historical development
and it has therefore become deeply embedded in the language of physics.
Secondly, the associated phenomena are much easier to understand
mathematically if we talk about these two vectors; the correct and
rigorous way to discuss electromagnetism is to use what is called the
electromagnetic field tensor, a single mathematical entity, but a
tensor is a more difficult concept to grasp. It is the nature of
electromagnetism that it cannot be fully described using a single
vector field, but two vector fields can contain the information which a
single tensor field does.

QUESTION:
I am a high school physics
teacher with a question concerning conductors. When a solid, conducting
cylinder is charged, the static charge will reside on the surface only.
When that same cylinder has moving charge (current), however, the
current distributes itself throughout the cylinder. Why the difference?

ANSWER:
First, there are two kinds of electrons on a
conductor: conduction electrons (typically on the order of one per
atom) and the remaining electrons bound to the atoms. Then one can
either add or subtract electrons to the material; this is the charge
which, when equilibrium is reached, must reside on the surface.
Similarly, if you put the conductor in an electric field, conduction
electrons will move around but they will eventually come to rest with
charge residing only on the surface. This is because if there is an
electric field inside the conductor the conduction electrons will move,
that is they will not remain at rest. Therefore, if you maintain an
electric field inside the conductor, electrons will move in response to
the force they feel and if you take them out on end and put them in at
the same rate at the other end, a steady current will flow through the
conductor. This is what a battery does: by maintaing a potential
difference (voltage) across the conductor it therefore maintains an
electric field inside the conductor which causes the charges to move.
(It also acts like a "pump" removing electrons from one end of the
cylinder and moving them to the other.)

So, in electrostatics the whole
conductor is at the same potential, the electric field is only outside
and perpendicular to the surface and all charge resides on the surface;
for a steady current a potential difference is maintained which causes
an electric field to exist inside the conductor which causes conduction
electrons to move through the volume.

QUESTION:
We are taught that E fields,
M fields and EM fields are real entities and that they contain an
energy density; and that (changes in) their influence propagate at
lightspeed. There is an equivalence of mass and energy, and energy must
be conserved. If these statement are all true, why is the mass of
charged matter (e.g., an electron) constant? Does there not exist a
continuous flow of energy radially outward from a static charge, for
example, as the influence of its electric field propagates to ever
larger volumes of space?

ANSWER:
Because a field has an energy density does
not imply that energy flows. In fact, if you compute the rate at which
energy leaves a volume surrounding a static charge, the answer is zero.
Charges radiate energy only when they accelerate and the energy loss is
taken from the kinetic energy of the accelerating particle, not its
rest mass energy.

QUESTION:
The textbooks of
physics state that 1 coulomb is a charge equal to 6.242x10^{18} electronic charges, and that the charge
of one electron is 1.602x10^–19 C. My question is: How did
the number 6.242x10^{18} come into
existence? What is its history? Did this number originate from a
measured quantity, that is, experimentally, or is it dirived
mathematically?

ANSWER:
What you are actually asking here is: "How is a Coulomb
defined and how can the charge, in Coulombs, of an electron be
measured?" (not to put words in your mouth, or anything!) It is
somewhat circuitous since the thing which is defined is the unit of
current, the Ampere (A), and the Coulomb (C) is defined in terms of the
Ampere. If you have two very long parallel wires each carrying equal
current I and separated by 1 m, the force per unit length (N/m,
newtons per meter) is 2 x 10^{-7} N/m when I= 1 A; that
is an operational definition of the Ampere. Now, a Coulomb is the
amount of charge which passes through a wire carring 1 A of current in
one second (s), so 1 A=1 C/s. That defines 1 C. Now, as you know,
electric charges exert forces on each other. It may be determined that
the force F (in N) felt by a particle with charge q _{1}
(in C) due to a charge q _{2}
(in C) which is a distance r (in m) away is F= 9x10^{9} (q _{1} q _{2} /r ^{2} );
this is called Coulomb's law. Now that you know the force law, you can
find the charge on an electron by measuring the force between two
electrons separated by a known distance. This charge turns out to be
1.6x10^{-19} C. If that is the number of coulombs per electron,
then the number of electrons per coulomb is simply the reciprocal,
1/1.6x10^{-19} =6.24x10^{18} .

QUESTION:
I teach AP physics in a high school in michigan, and can't seem to
reconcile these two facts: The electric field due to an infinite
conducting sheet with surface charge density sigma is
E=sigma/Epsilon_0. If I introduce an oppositely charged infinite
conducting sheet facing the original, by superposition, I get that the
field between them should be double in strength, i.e. E=
2*sigma/epsilon_0. However, gauss's law, using a cylinder with one flat
face between the sheets and one face within one of the conducting
sheets still gives me E=sigma/epsilon_0. Where is the flaw in my logic?
When I look at the field lines, I see that the oppositely charged
infinite sheet doesn't introduce more, since every positive charges
field line on the positive sheet must end on a negative charge, either
at infinity or on the negative sheet, but that doesn't explain to me
why superposition doesn't seem to work here.?

ANSWER:
The problem you are having is rather straightforward. You are
correct in saying that with two sheets the field is twice as large
between the plates; however, the field outside the plates, also by your
superposition argument, is zero. Thus, when Gauss's law is applied
there is no flux leaving the surface outside, which gives twice the
field inside: e _{0} E _{1} *(2*A )=s A with one plate
and e _{0} E _{2} *A =s A with two, so E _{2} =2*E _{1}

QUESTION:
You can discharge a metal conductor which has been charged by static
electricity by "connecting it to the ground with a metal strip" - can
this also be done a work for charged insulators? If so or not, why?

ANSWER:
No. On a perfect insulator the charges are not free to move, so
even if they have a path to a place with lower electric potential, they
are not free to move. Of course, there is no such thing as a
perfect insulator and charge will slowly leak off. For a
conductor, excess electric charge is perfectly free to move; that is why
all excess charge on a conductor is always located at the surface.

QUESTION:
We always talk about charging up "insulators" via static electricty.
(ie - through friction) Does it work for conductors? Does it still
remain a surface phenominum? Does the metal remain charged afterwards?
Does it dissapate naturally?

ANSWER:
Yes, conductors can become charged via static
electricity. For a conductor, all excess charge must reside on
the surface whereas, for an insulator, you may have charge
inside. The metal, in the real world, will discharge by leaking
its charge either to the air around it or through whatever (imperfect)
insulators may be supporting it. Even if it is perfectly isolated
from its environment, a metal will leak its charge away from any place
on its surface where the electric field (due to the excess charge) is
strong enough (this is called corona discharge); for example, a very
sharp needle will have a very strong electric field at the point and
electrons will stream away (or toward) this point.

QUESTION:
Consider two charged particles traveling in equal but
opposite directions as shown on the website at www.hypercomplex.us/Questions/bforce.htm .
In a reference frame in which both charges are moving, the second
charge experiences a magnetic force with non-zero magnitude resulting
from the magnetic field produced by the first. The magnitude of this
force, however, becomes zero when the velocities are transformed to a
reference frame in which the velocity of either charge is zero. Why
does the force disappear given this transformation of coordinates?

ANSWER:
There are a couple of problems with this web page.
First of all, the magnetic field given is incorrect. This is not
a magnetostatic situation which means that the magnetic field is not
constant with time at every point in space. The actual field must
be computed at the 'retarded time', which takes into account the time
it takes the field information to propogate to the second charge (at
the speed of light); however, the given field is approximately true if
the speeds are small compared to the speed of light (which is called a
'quasistatic' situation). The second problem is that the Coulomb
force between the two particles is totally ignored. I would guess
that part of your problem conceptually here is that you are finding a
particle with no force in one frame and with force in another. If
you remember that there is also an electrical force, then you will not
have this problem. Because the magnetic force depends on the
velocity of the charge, then it should be obvious and not disturbing
that there will be some frame where the magnetic force is zero.
The correct transformation of magnetic and electric fields from one
frame to another is a topic in electromagnetism which is quite advanced
and the details are beyond the scope of what 'Ask the Physicist' is
supposed to be about.

Here is a
similar example of magnetic forces going away. In this case it is
the field itself which I can make disappear. Imagine a long line
of electric charge at rest. Obviously, there is no magnetic field
but there is an electric field. Now imagine making the whole line
move with some speed v ; you now have a long straight
current and therefore a magnetic field has appeared. The electric
field will increase because the charge density on the line will
increase because of length contraction.

QUESTION:
If you bring a compass to the right side of a bar magnet (the
north is on the right, and the south is on the left of the bar magnet),
which way should the compass needle point? To the left (away from the
north pole of the magnet), or to the right (so it touches the north
pole of the magnet)

ANSWER
A compass is itself a bar magnet and the end which points
north is, by convention, called the north pole of the compass
(magnet). Now, as you probably know, like magnetic poles repel
and opposite magnetic poles attract. Therefore the north end of
the compass will be repelled by the north pole of the magnet so the
compass will point away from the magnet. Incidentally, note that
the convention means that the magnetic north pole of the earth is
actually a magnetic south pole if the north pole of the compass points
to (is attracted to) it.

QUESTION:
Where can I find information on current patways in seawater?
In response to a DARPA request for submarine detection, I thought I
might be able to detect a submarine in shallow water by the change in
conductivity when a submarine passed between two electrodes, about 200
feet apart. But if it was that easy, the Navy would have done it a
century ago.
I read up on it a bit and tried the Feynman Lectures on Physics, which
I find to difficult on my own. But I read that conductivity is
proportional to the area of the conductor, and inversely proportional
to the length. A submarine passing between two electrodes effectively
changes the pathlength between them, which I had hoped to detect. But,
my guess is that the current passing between the two electrodes would
in fact remain constant, because because it is free to move through a
greater area to compensate for the change in pathlength.

If you
could tell me where to look for information in how to model this
mathematically, I'd appreciate it. I've read up on div, grad, and curl,
but don't see how to set up the equations to account for when an object
is present or absent in a field.

ANSWER:
This is an interesting question. The answer can be
found in a problem in the well-known textbook on electricity and
magnetism, Introduction to Electrodynamics by David J.
Griffiths (Prentice-Hall); it is problem #1 in chapter 7. Here
the student is first asked to compute the resistance between two
concentric metal spheres of radii a and b (b >a )
where the volume between the two spheres is filled with a conducting
material with conductivity s.
The
answer is R= [(1/a )-(1/b )]/(4 ps ). Why is this
interesting? Because if b >>a , it is, to a
superb approximation, given by R= 1/(4a ps ), completely
independent of the size of the outer sphere. So we can say that
the resistance between the inner sphere and a point infinitely far away
is essentially the same as the resistance between the inner sphere a
point 100a away; the resistance is nearly completely determined
by the water near the inner sphere. So the way you measure the
conductivity of seawater is to put two small spheres a large distance
apart, maintain a constant potential difference between them, and
measure the current which flows. Since the current which flows is
determined by the resistances (1/(4a ps ) for each or 1/(2a ps ) net) and the
resistances are due only to the water near the spheres, then unless the
submarine passes very close by one of the spheres (in which case you
could see or hear it so you wouldn't need your fancy detector!), it
will have no effect on the current.

Where you
need to do your research is in the computation of resistance. You
see, although the "length" you refer to above is just (b-a ), the
"area" you refer to is changing as you move out, so you have to
integrate, not just multiply area times length.

QUESTION:
After using google to search countless web sites, I still
can't find the answers to the following questions.

How
permanent are permanent magnets?
If 2
permanent bar magnets are place in a way that their "north" pole face
each other (causing them to repell each other), will their polarity
change?
How do
you calculate (or measure) the strength of a permanent magnet and
electromagnets.
ANSWER:
Well, of course, nothing is truly permanent.

What
makes a permanent magnet (PM) permanent? In a normal piece of
material from which the PM is made, there are regions small compared to
the whole piece but large compared to atomic scales which are called
domains. In these domains, the magnetic moments of many electrons
are all aligned in one direction so the domain is, itself, a tiny
permanent magnet. However, these domains are all randomly
oriented relative to each other so the piece of stuff is not itself a
permanent magnet. The trick is to get all the domains to align
with other. The only way I know to accomplish this is by brute
force--put it in a very strong magnetic field. Some materials,
like just pure iron, will become magnetized but when the magnetizing
field is turned off the domains will tend to migrate back
toward what they were so the iron will be a weak PM which will, over
time become weaker. Many other materials are more suitable as PMs
because, after being magnetized they tend to stay magnetized.
Nevertheless, over a long time they will tend to become
weaker.
A second way that a PM can lose its magnetization is if it is heated
up. When a PM reaches a temperature called the Curie temperature
(CT), all magnetization is lost and it will cool back down to an
unmagnetized state. In fact, even heating a PM up to a
temperature which is lower than the CT will lead a more rapid decay of
its magnetization than would happen at cooler temperatures.
If a
magnetic field can cause magnetization, then it certainly can change it
also. Putting these two PMs together like this would cause both
to become more weakly magnetized but, because the fields of individual
PMs are considerably smaller than the fields which magnetized them in
the first place, the effect would likely be small.
The
strength of a magnetic field depends on lots of things--not just how
magnetized the magnet is but on the shape of its poles, how far you are
away from it, etc . I presume that you are just interested
in how to measure a magnetic field. You can buy commerical
gaussmeters or build
your own . You just stick the probe in the region where you
want to measure the field and read it off a meter. How do they
work? Several ways which I will not give details of how they work
since you could look them up: (a) the Hall effect where a voltage is
generated when a known current passes through the probe in a magnetic
field; (b) a rotating coil in which there is an induced current when it
is in a magnetic field (like how a generator works); (c) nuclear
magnetic resonance in which magnetic moments of nuclei flip when
exposed to electromagnetic waves of just the right frequency.
Another way would be to measure the force on a current carrying wire or
the torque on a tiny bar magnet (little compass).
QUESTION:
Who first measured the wavelength of one electromagnetic wave
and how?

ANSWER:
Credit is usually given to Dr. Thomas Young
(1773-1829). Most famous of his "measurements" is the so-called
double slit diffraction experiment in which light strikes two closely
spaced slits in an opaque sheet. Each slit acts like a source of
waves and these two waves interfere with each other when they strike a
screen some distance away. What interference means, essentially,
is that the two waves add up to give a net disturbance at that
point. So, if the two waves are both at a crest they add up to
look twice as big (therefore bright) but if one is at a crest and the
other is at a trough, they will cancel each other out and there will be
no light. Young explained many well-known optical phenomena (such
as the colored fringes you see from an oil slick) using the idea of
interference; he and his ideas were, as often happens with
revolutionaries, reviled by many of his contemporaries. Before
Young, Christiaan Huygens (1629-1695) was an advocate for a wave model
of light; he was able to show that light must slow down in a medium
like glass and thus explained refraction. Some 13 years after
Young had described interference, Augustin Jean Fresnel (1788-1827)
independently developed the notion of interference.

QUESTION:
I'm a chemist who's having a tough time getting his
head around a little electric field problem. Here's the
deal - I've got a supramolecular system that orders itself into 3
nm "tubes". The surface of the tube is made up of the ionic ends
of molecules and form a positive and the corresponding negative
layer (i.e. a dielectric). I wanted to make the tubes line up
perpendicular to the substrate I've made them on, and I have, by
putting the film into a capacitor i.e. 2 copper plates 4 mm apart
with 3000 volts between them. The question is, why does this
work? I'm glad to give any further clarifications you may
require. I originally thought this would be a simple problem, but
have been stumped at each step.
QUESTION TO THE
QUESTIONER:
I'm not sure I understand the problem or the question! If I
had one of your tubes in empty space, describe the charge density
on it to me; e.g. positive charge distributed uniformly on the
outer surface and net negative charge inside the tube such that
the net charge is zero? Is there any net charge on the ends of
the tube? How do you know that they all stand up straight? Why do
you call it a dielectric? Maybe you mean dipole? What happens if you
reverse the field?
REPLY:
First, thanks for your speedy response. Second, perhaps more
detail is required. I have a micelle (the tube) which is made of many
long alkyl chains with amino groups (which is positively charged) at
the terminus. Charge is balanced with chloride ions (negative).
Surrounding the micelle is silicate (another different dielectric),
which is only partially polymerized, and still flexible. We apply the
field, the silicate continues to condense, we remove the field and the
shape is stuck. The ends of the tubes are the ends of the micelle,
which will have no net charge, we know they stand straight by TEM
images of the silicate after the procedure, there are dipoles in the
system, but I don't think they contribute much to these supramolecular
events, and reversing the field produces the same end product.

ANSWER:
My suspicion is that the answer to your question is, in fact,
totally independent of all the details you have given me. Imagine a
needle in a uniform electric field. If the needle is made of a
dielectric material, the needle will become polarized throughout its
volume but the ostensible effect will be for each end of the needle to
become electrically charged (the ends having opposite charges). The net
effect of this charge will be for there to be a net torque on the
needle which will tend to align it with the field; indeed, this will
happen regardless of the direction of the field (which is why I
asked!). This same thing would happen with a conducting needle except
the end charges would be due to real electrons migrating to one end and
leaving positive ions at the other end. I believe that this explains
your effect. Of course when you turn off the field, the polarization
goes away; it sounds like the silicate gives rigidity to your tubes so
that they remain in position after the field is turned off.