Magnetic force between moving charged particles

[Cecil]

This situation arose in physics class today. My prof put the following question on the overhead and had us discuss it:

Two positively charged particles, q1 and q2, have the same velocity v. What forces does q2 feel?

a) No forces
b) Electric force only
c) Magnetic force only
d) Both electric and magnetic force.

I thought the answer was b, since q1 is stationary w.r.t. q2 and thus doesn't produce a magnetic field affecting q2. My prof then said the correct answer was d, and when I called him on it, dodged the question by saying that it didn't matter whether q2 was moving or not, q1 was moving and so produced a magnetic field.

This to me is patent nonsense. From the POV of an observer on a train with velocity v, q1 and q2 are stationary charges, and so there is clearly no magnetic field.

The problem I have arises when I think about the forces involved. If we consider q1 to be above q2, it clearly exerts a downward electrical repulsive force on q2. But, q1's motion wrt a stationary observer looks like a current, and so produces a magnetic field. Why does this field not have an effect on q2, a particle which is moving perpendicular to a magnetic field? Why should the force due to the motion of a charged particle through a magnetic field depend on the origin of the field?

My prof said he'd think about it (read: research it) and come back on Friday with a better answer. I want to have something to say back to him. Can some of you physics guys help me out here?

[Terry]

I think the correct answer depends on the reference frame.

--Terry

[kalen]

Solving the problem from both points of view should give no contradictions.

To solve the problem, the observer on the train will have it the easiest as he doesn't have to worry about a current from moving charges (at least for the first moment). It is then an easy to transform back to the stationary frame and you're done.

[Terry]

Solving the problem from both points of view should give no contradictions.

But in one frame, the force would be partly magnetic, and in the other it wouldn't. Same total force, of course.

I could be wrong...

--Terry.

[Cecil]

But the electric force doesn't depend on the relative velocity between the particles, so it would seem that the force is different depending on the reference frame.

[Dilb]

This (almost) precise problem is sitting in front of me in my reletivity book.

For electrons moving parallel to each other, separated by r:
The electrons experience an electric force of

F = (1/gamma)*(k*q*q/r^2)

where gamma is the Lorentz factor.

They also experience a magnetic force

F = ((1/gamma) - gamma)(k*q*q/r^2)

So, yes, from a certain reference point they experience both forces. Since you probably want to know about your personal reference frame, there is a magnetic force to consider.

[Schneibster]

This situation arose in physics class today. My prof put the following question on the overhead and had us discuss it:

Two positively charged particles, q1 and q2, have the same velocity v. What forces does q2 feel?

a) No forces
b) Electric force only
c) Magnetic force only
d) Both electric and magnetic force.

I thought the answer was b, since q1 is stationary w.r.t. q2 and thus doesn't produce a magnetic field affecting q2. My prof then said the correct answer was d, and when I called him on it, dodged the question by saying that it didn't matter whether q2 was moving or not, q1 was moving and so produced a magnetic field.Actually, the professor is both right and wrong. According to Einstein, an observer who is motionless with respect to the two particles (comoving with them, in other words) will see a different situation than an observer for whom the two particles are moving at equal, non-zero velocities (remember, velocity is a vector- so this means not only the same speed, but in the same direction). The first observer will observe only electrostatic effects; the second observer will also observe a magnetic effect. Interestingly, this difference in this particular pair of frames of reference precisely accounts for the difference in the force between the particles just sufficient to make them move more slowly as required by time dilation due to their motion; in other words, the magnetic force between them is attractive, and offsets the electric force repulsion, just enough to account for their slower motion due to time dilation of their frame of reference due to its relativistic motion! Thus, we see that magnetism is actually a relativistic effect due to the motion of the particle that is the source of the magnetic field relative to the particle that feels the force of the field.

This to me is patent nonsense. From the POV of an observer on a train with velocity v, q1 and q2 are stationary charges, and so there is clearly no magnetic field.Precisely correct. And the time dilation of this observer with respect to the observer for whom q1 and q2 are moving precisely accounts for the difference in motion and thus the difference in force. To put this another way, magnetism is a pseudo-force resulting from the combination of the electric force and time dilation.

The problem I have arises when I think about the forces involved. If we consider q1 to be above q2, it clearly exerts a downward electrical repulsive force on q2. But, q1's motion wrt a stationary observer looks like a current, and so produces a magnetic field. Why does this field not have an effect on q2, a particle which is moving perpendicular to a magnetic field? Why should the force due to the motion of a charged particle through a magnetic field depend on the origin of the field?What is really happening is that due to relativistic effects, the effect of the force of the electric field on q2 appears to be lessened, that is, its motion due to the repulsive force happens more slowly; this is interpreted as an opposing, attractive force partly offsetting the repulsive electric force, IOW, magnetism. Thus, magnetism is a pseudo-force that is actually the relativistic effect of time dilation offsetting the effects of the electric force.

My prof said he'd think about it (read: research it) and come back on Friday with a better answer. I want to have something to say back to him. Can some of you physics guys help me out here?The above should help.

You should also learn from this that the very existence of the magnetic field and its relationship to the electric field is due to relativity; yet another way in which relativity underlies all of physics. This pseudo-force is just as real and sensible in its effects as the centrifugal pseudo-force you feel on a merry-go-round, or that the stone feels in a sling. And they are similar, particularly in the case of the permanent magnet: the permanent magnet shows a net magnetic field because of the unmatched spins of the electrons in the outer shells of atoms that make it up, and because these spins get lined up with one another as they are rotated over time by the Earth's magnetic field, thus multiplying the magnetic field strength.

Have fun, and I hope I helped you learn something. And be nice to the professor; I'm guessing you're not learning this in a relativistic physics class!

[epepke]

Actually, the professor is both right and wrong.

In any event, it's a terrible question. Sometimes it may be desirable to use classical mechanics, as in classical electromagnetism, to simplify things. But when you start writing questions that encourage people not to understand relativity, that's going too far.

Thus, we see that magnetism is actually a relativistic effect due to the motion of the particle that is the source of the magnetic field relative to the particle that feels the force of the field.

This is the key to understanding the whole mess. Magnetism is just charge plus Einsteinian relativity. Historically, the whole impetus for Einstein was to make some of the predictions of Maxwell's equations work out. Mathematically, however, you can work out Maxwell's equations given Einsteinian relativity and just the basics about electrical charge.

[pgwenthold]

If they have the same charge, then I would argue that for an external observer, they create an equal and opposite magnetic force on each other, such that there is no net force between them. The magnetic field created by one is in the opposite direction of that created by the other. Since they are both moving the same way, one will be attractive but the other will be repulsive. If they are the same charge, with same velocity, magnitude of the forces are equal, so they cancel.

From the reference frame of the charges, there is no net force, either. So we get the same results in both frames of references.

I need to think about the case of unequal charges.

[CBL4]

My physics is rusty and never was that good but here are my, quite likely incorrect, thoughts:
1) If they have the same speed but different directions, they will have relative motion and the magnetic force will apply.
2) If they have the same speed and direction, the electrical charge will cause the directions to change and they will no longer have the same direction.

Therefore except possible for an instant, both forces will apply.

CBL

[Dilb]

If they have the same charge, then I would argue that for an external observer, they create an equal and opposite magnetic force on each other, such that there is no net force between them. The magnetic field created by one is in the opposite direction of that created by the other. Since they are both moving the same way, one will be attractive but the other will be repulsive. If they are the same charge, with same velocity, magnitude of the forces are equal, so they cancel.

From the reference frame of the charges, there is no net force, either. So we get the same results in both frames of references.

I need to think about the case of unequal charges.


Note: I'm talking about parallel (side by side) particles, since that's what I have a nice example for.

No, the magnetic force does change the net force. Each particle, in our frame of reference, creates a magnetic field which is perpendicular to the particles motion (point your thumb in the direction of current, your fingers curl around in the direction of the field). The other particle experience this field and feels a slight attraction force towards the first particle (assuming they are both positive or both negative). This is like the attractive force that 2 current carrying wires feel when placed parallel to each other.

So to compensate for reletivity effects, the magnetic force slightly reduces the attractive force that we see acting on each particle.

If I understand the vector stuff, the magnetic force a particle feels depends on the velocity being perpendicular to the electric field it's in. For 2 particles moving on a single line (one particle immediatly behind the other), there is no magnetic force in our frame, and naturally there's a bunch of complicated vector calculus for everywhere inbetween.

[69dodge]

If they have the same charge, then I would argue that for an external observer, they create an equal and opposite magnetic force on each other, such that there is no net force between them. [...] If they are the same charge, with same velocity, magnitude of the forces are equal, so they cancel.
The two forces have equal magnitude and opposite direction, but they don't act on the same body, so they don't cancel. The magnetic field generated by one charge exerts an attractive force on the other charge, and vice versa. So the two charges accelerate toward each other due to their magnetic fields. Or rather, they accelerate away from each other less rapidly than the strong repulsive electric force between them would indicate.

The magnetic field generated by a moving charge doesn't exert any force on the charge itself; it just exerts forces on other moving charges.

The magnetic field created by one is in the opposite direction of that created by the other. Since they are both moving the same way, one will be attractive but the other will be repulsive.
"Attractive" is not a fixed direction; it just means "toward the other charge." For the charge on the left, "right" is attractive; for the charge on the right, "left" is attractive. So, the two magnetic forces are both attractive, even though they're in opposite directions.

[Ziggurat]

This situation arose in physics class today. My prof put the following question on the overhead and had us discuss it:

Two positively charged particles, q1 and q2, have the same velocity v. What forces does q2 feel?

a) No forces
b) Electric force only
c) Magnetic force only
d) Both electric and magnetic force.

I thought the answer was b, since q1 is stationary w.r.t. q2 and thus doesn't produce a magnetic field affecting q2. My prof then said the correct answer was d, and when I called him on it, dodged the question by saying that it didn't matter whether q2 was moving or not, q1 was moving and so produced a magnetic field.

The relativity issue people have mentioned is quite important (the correct answer changes depending on reference frame, but the total force ends up the same), but there's another issue nobody mentioned yet: the problem, as stated, is incompletely specified. Depending on the relative positions of the particles (in particular, if they line in a line along the direction of motion), then they may not feel any magnetic field from each other. So if that wasn't specified, then it's not possible to give an answer (other than a and c always being wrong).

[Dilb]

The relativity issue people have mentioned is quite important (the correct answer changes depending on reference frame, but the total force ends up the same), but there's another issue nobody mentioned yet: the problem, as stated, is incompletely specified. Depending on the relative positions of the particles (in particular, if they line in a line along the direction of motion), then they may not feel any magnetic field from each other. So if that wasn't specified, then it's not possible to give an answer (other than a and c always being wrong).

I mentioned that, even if I wasn't very confident in it.

[Cecil]

The relativity issue people have mentioned is quite important (the correct answer changes depending on reference frame, but the total force ends up the same), but there's another issue nobody mentioned yet: the problem, as stated, is incompletely specified. Depending on the relative positions of the particles (in particular, if they line in a line along the direction of motion), then they may not feel any magnetic field from each other. So if that wasn't specified, then it's not possible to give an answer (other than a and c always being wrong).
I fear this is my fault. The professor did have a diagram showing two particles travelling parallel to each other with some separation between them.


If my understanding is correct, then, the force between the particles is the same in all reference frames, though depending on the particular frame chosen some of the force will be seen as electric and some as magnetic.

I realise that the magnetic force is merely a pseudo-force caused by the reduction in strength of the electric force at relativistic velocities. The problem I have now is: how do permanent magnets work?

I know that permanent magnets create a magnetic field because the unpaired electrons in the outermost orbital of each atom of a ferromagnetic material find they can co-exist in a lower energy state if they all have the same spin. But in this case there doesn't seem to be any relative motion between, say, a bar magnet and an iron filing, both of which are electrically neutral. Where does the magnetic force come from?

[GodMark2]

I know that permanent magnets create a magnetic field because the unpaired electrons in the outermost orbital of each atom of a ferromagnetic material find they can co-exist in a lower energy state if they all have the same spin. But in this case there doesn't seem to be any relative motion between, say, a bar magnet and an iron filing, both of which are electrically neutral. Where does the magnetic force come from?

Think not of the relative motion of the magnet to the iron filing, but rather to the relative motion of the electrons in that magnet to the electrons in the filing. If all of the electrons are in random spin states, than the sum of their motions is near zero, but when they are in lock-step, the sum of those individual motions becomes significant.

[Cecil]

Think not of the relative motion of the magnet to the iron filing, but rather to the relative motion of the electrons in that magnet to the electrons in the filing. If all of the electrons are in random spin states, than the sum of their motions is near zero, but when they are in lock-step, the sum of those individual motions becomes significant.
But the electrons aren't "really" moving, are they? I thought electrons were supposed to be considered as a probability cloud.

As is probably obvious, I know just enough theoretical physics to be dangerous. :p

[epepke]

But the electrons aren't "really" moving, are they? I thought electrons were supposed to be considered as a probability cloud.

As is probably obvious, I know just enough theoretical physics to be dangerous. :p

I think that you're thinking of electron densities.

You're right that's what they are. But they also move.

I once did a visualization of some slow near collisions between electrons, positrons, protons, etc. for some chemists, where only the density was visualized. Not only do they move, but they do a little do-si-do around each other when they pass close.

[Ziggurat]

I think that you're thinking of electron densities.

You're right that's what they are. But they also move.


This can actually get kind of messy. Electrons can have orbital moments (the "cloud" rotates around the atom in one direction), but only in some materials. But they always have spin moments. There isn't really a good way of thinking about this classically, since an electron is (as close as we can measure) a point-like particle. But it's got quantized angular momentum, and that means that it's also got a magnetic moment, even when completely stationary. That moment, when unpaired with an electron in the oposite spine state, is what usually creates macroscopic magnetism in materials.

[epepke]

This can actually get kind of messy. Electrons can have orbital moments (the "cloud" rotates around the atom in one direction), but only in some materials. But they always have spin moments. There isn't really a good way of thinking about this classically, since an electron is (as close as we can measure) a point-like particle. But it's got quantized angular momentum, and that means that it's also got a magnetic moment, even when completely stationary. That moment, when unpaired with an electron in the oposite spine state, is what usually creates macroscopic magnetism in materials.

Yes. It gets very messy and very non-classical. And there's spin, so there is a magnetic moment. And the damn things don't appear to rotate in place, but they do carry off angular momentum with spin, such as in that experiment with cold cobalt and an electromagnet back in the 50s that showed violation of P-symmetry.

However, I'm presuming that the OP was dealing with classical electromagnetism, which pretty much ignores this.

And besides, they move. If you set up a CRT, well, yeah, the electrons are moving.

[Schneibster]

I fear this is my fault. The professor did have a diagram showing two particles travelling parallel to each other with some separation between them.

If my understanding is correct, then, the force between the particles is the same in all reference frames, though depending on the particular frame chosen some of the force will be seen as electric and some as magnetic.You are asking the right questions; and you will "get it" before long and have an experience that many here enjoy greatly: the "Eureka moment." It's very similar to what made Vin Diesel say, "I live for this s**t!" in that movie. :D

Here's the deal:
f = ma
v = at
d = vt
Which implies that force is doubly dependent upon time. If Lorentz symmetry says that time dilates in frames at different velocities than the observer's, what is the effect on the observer's measurement of force in a different frame? For this reason, your statement, "...the force between the particles is the same in all reference frames" is wrong, but it is interestingly wrong.

I realise that the magnetic force is merely a pseudo-force caused by the reduction in strength of the electric force at relativistic velocities. This is cognitive dissonance; you're very, very close to understanding this. You understand it intellectually, but you haven't yet seen the implications.

The problem I have now is: how do permanent magnets work?

I know that permanent magnets create a magnetic field because the unpaired electrons in the outermost orbital of each atom of a ferromagnetic material find they can co-exist in a lower energy state if they all have the same spin. But in this case there doesn't seem to be any relative motion between, say, a bar magnet and an iron filing, both of which are electrically neutral. Where does the magnetic force come from?This is due to another implication. There actually is both electrostatic interaction between the "neutral" filing and bar magnet, and relative motion. Think how the unpaired electrons in the outer shells of all those iron atoms in the bar magnet will mostly all be revolving in the same direction, with their spin axes pointing in the same direction too. Now imagine all the unpaired electrons spinning at random angles to the collective electrostatic force generated by the sychronized motions of the unpaired electrons in the bar magnet- you will see the unbalanced forces that must result, pulling thisaway at this instant, pushing thataway at that instant; and repeating over and over again. Now imagine all those atoms aligning themselves so that the parts getting greater force than the average move farther away, the parts getting lesser force than the average move closer, and the parts getting the average stay where they are. This all adds up to a collective force on the iron filing- which orients itself so that the maximum number of atoms feel the average force!

Badda-boom, badda-bing, your iron filing aligns itself with the "magnetic lines of force" just as if they were real physical entities rather than artifacts of the relativistic effects of the spinning, revolving electrons!

I have always thought that magnetism is very cool for this reason. It illustrates for me a general principle of how things work. The underlying symmetries of relativity and Maxwell's equations combine to create something with a great deal of the type of beauty one finds in, say, the expression of a fractal function in the growth of cauliflower.

[goodgirlonhere]

Let me put this into perspective...or layman's terms. I've actually never taken physics but I am an electrician.;) Magnetism is something heavily studied in Industrial Electricity.
Think of your answer as you and a friend driving 2 cars. One car is q1 the other q2. Both of you drive the SAME speed limit side by side on the highway. This would be your "Velocity" in the equation. Now both of you will have the radio playing extremely loud. This would be your "Positive charges". Now stick your hand out the window. What would you "feel"? You would feel a magnetic effect and electrical. The electrical would be the "beat" of the music playing and the magnetic would be the "pull" between the two cars or the "wind". Thus in conclusion q1 and q2 travelling at the SAME velocity would feel a magnetic and electrical field.
Now how is that for perspective?:cool:

[luvhumility]

I will just ask one little question about this e field and b field discussion. How can a perm "magnet" that is assumed to have some "force" in and of itself "attratc" other ferromagnetic materials (iron) without the other outside attractee being interactively involved in the process? I feel that magnets do not "create" this magnetic force but just transform or transmutate other forces in "the ether" in a more efficient manner than other materials or structures. similar to how a quartz crystal can produce "E fields" when vibrated. (Actually they do it constantly)! the cosmos ALLWAYS are moving as is Everything in it! I do not really know but I suspect EM theory/math is ready fo some serious upgrades. Keep asking the good questions ALL!

[epepke]

I will just ask one little question about this e field and b field discussion. How can a perm "magnet" that is assumed to have some "force" in and of itself "attratc" other ferromagnetic materials (iron) without the other outside attractee being interactively involved in the process? I feel that magnets do not "create" this magnetic force but just transform or transmutate other forces in "the ether" in a more efficient manner than other materials or structures. similar to how a quartz crystal can produce "E fields" when vibrated. (Actually they do it constantly)! the cosmos ALLWAYS are moving as is Everything in it! I do not really know but I suspect EM theory/math is ready fo some serious upgrades. Keep asking the good questions ALL!

Sorry, but this is word salad, and I hate word salad.

As far as I can tell, you're asking why a permanent magnet can attract a piece of iron (or another material).

I don't know exactly what "the other outside attractee being interactively involved" is supposed to mean, but as far as I can tell, it's not true.

A piece of iron changes when it is in a magnetic field, and the attraction is due to the change. Specifically, it becomes temporarily magnetized itself in just the right way to attract and become attracted to the other magnet.

If it is ferromagnetic, which iron of course is, and you leave it in contact long enough, it will become permanently magnetized.

Now, if you're clever enough, you can conclude from this that a permanent magnet will weaken over time. This is, of course, true. It weakens faster if it's heated, and once heated to the Curie point, all bets are off. But even at room temperature, magnetic tape and permanent magnets made of solid iron will degrade over time.

[epepke]

This is cognitive dissonance; you're very, very close to understanding this. You understand it intellectually, but you haven't yet seen the implications.

Here is the explanation I usually give about this:

Special Relativity shows Lorentz contraction. Moving objects shorten in the direction of travel. How would you test this?

You could make a ruler with a bunch of tic marks on it and shoot it by. You could then take a camera and take a snapshot of a sufficiently small length of the ruler from sufficiently far away. You would expect to see more tic marks on the ruler than if it were stationary.

Of course, it's hard to make a ruler go that fast, and you need a good shutter finger.

So instead of tic marks and a camera, you use electrons and protons. They're cheap. You can get a bunch of them for a dollar.

You put two copper wires next to each other and hook them up to a battery. The electrons move, but the protons don't.

So what does a proton in one wire "see" in the other wire? It sees a bunch of protons, stationary. It's repelled by the protons. It also sees a bunch of electrons moving. It's attracted to them. But since the electrons are moving along, the space between them is Lorentz-contracted. So, nearby, the proton will see more electrons than protons, just like you'd see more tic marks on a ruler.

So the proton will be attracted to the electons in the other wire, and the wires will be attracted to each other. Of course, this is exactly what happens, and that's called a magnetic field.

Same for the electons. The electrons in each wire will "see" the electrons in the other wire as being roughly stationary, but it will see the protons moving in the opposite direction.

Of course, iron has more than one electron and proton per atom, and only some of the electrons are moving at any one time, but the rest can be ignored, as they don't "see" or "feel" anything unusual.

Also of course, each electron will "see" more protons than electrons in its own wire. That's related to the phenomenon called "resistance." Electrons in the band structure will drop into lower energy states, releasing energy. You can see the energy coming from an incandescent light bulb, but mostly, they just make heat. In a metal, the electrons have a band structure, which means that they sort of blob together in a quantum way, providing many more energy states than you would expect by looking at just one atom. This is why even extremely thin metal foil is still opaque to visible light. As long as there are enough atoms to support the band structure, the electron band reflect light as usual. You have to get them ridiculously thin to get rid of the band structure, at which point they become transparent. You can also mess up the band structure by getting a metal really cold, which leads to superconduction. The band structure is also why metals have such a high heat capacity. But I'll stop now.

[Cecil]

You are asking the right questions; and you will "get it" before long and have an experience that many here enjoy greatly: the "Eureka moment." It's very similar to what made Vin Diesel say, "I live for this s**t!" in that movie. :D

Here's the deal:
f = ma
v = at
d = vt
Which implies that force is doubly dependent upon time. If Lorentz symmetry says that time dilates in frames at different velocities than the observer's, what is the effect on the observer's measurement of force in a different frame? For this reason, your statement, "...the force between the particles is the same in all reference frames" is wrong, but it is interestingly wrong. Well, in a moving reference frame the time dilates by a factor of sqrt(1 - v^2/c^2), but mass also increases by the same factor, so the force in a moving frame is reduced by a factor of sqrt(1 - v^2/c^2). So the total force between parallel particles is less if you're moving relative to them than if you're comoving with them. But in order for the magnetic force to be perceived, the Coloumb force has to be decreased by a larger factor than that. But since that force is kqq/r^2, none of which change in moving frame, where does this reduction come from?

Oh, I think I see it. The virtual photon carrying the electromagnetic force only travels at c, so the "distance" between the particles as seen by the photon, and for the purposes of force calculation, would be ... (*scribble scribble pythagoras scribble*) r = r0^2/sqrt(1 - v^2/c^2), and since the force is proportional to 1/r^2, the electric force decreases by a factor of 1 - v^2/c^2.

So when comoving particles are viewed from a moving frame, the total force decreases, but not by as much as the Coloumb force. The "magnetic force" is what makes up the difference.

Weird.

This is cognitive dissonance; you're very, very close to understanding this. You understand it intellectually, but you haven't yet seen the implications. Is the above the implications? :D

This is due to another implication. There actually is both electrostatic interaction between the "neutral" filing and bar magnet, and relative motion. Think how the unpaired electrons in the outer shells of all those iron atoms in the bar magnet will mostly all be revolving in the same direction, with their spin axes pointing in the same direction too. Now imagine all the unpaired electrons spinning at random angles to the collective electrostatic force generated by the sychronized motions of the unpaired electrons in the bar magnet- you will see the unbalanced forces that must result, pulling thisaway at this instant, pushing thataway at that instant; and repeating over and over again. Now imagine all those atoms aligning themselves so that the parts getting greater force than the average move farther away, the parts getting lesser force than the average move closer, and the parts getting the average stay where they are. This all adds up to a collective force on the iron filing- which orients itself so that the maximum number of atoms feel the average force!

Badda-boom, badda-bing, your iron filing aligns itself with the "magnetic lines of force" just as if they were real physical entities rather than artifacts of the relativistic effects of the spinning, revolving electrons!

I have always thought that magnetism is very cool for this reason. It illustrates for me a general principle of how things work. The underlying symmetries of relativity and Maxwell's equations combine to create something with a great deal of the type of beauty one finds in, say, the expression of a fractal function in the growth of cauliflower. That's awesome. I need to think about that some more.

Please, say more cool stuff like that.

[Cecil]

Same for the electons. The electrons in each wire will "see" the electrons in the other wire as being roughly stationary, but it will see the protons moving in the opposite direction. This is also why wires with opposite currents repel, right? Because the space between the moving electrons is contracted more than the space between the more-slowly-moving protons, so the net force is a repulsive one?

Also of course, each electron will "see" more protons than electrons in its own wire. That's related to the phenomenon called "resistance." Electrons in the band structure will drop into lower energy states, releasing energy. You can see the energy coming from an incandescent light bulb, but mostly, they just make heat. In a metal, the electrons have a band structure, which means that they sort of blob together in a quantum way, providing many more energy states than you would expect by looking at just one atom. This is why even extremely thin metal foil is still opaque to visible light. As long as there are enough atoms to support the band structure, the electron band reflect light as usual. You have to get them ridiculously thin to get rid of the band structure, at which point they become transparent. You can also mess up the band structure by getting a metal really cold, which leads to superconduction. The band structure is also why metals have such a high heat capacity. What's band structure?

But I'll stop now. Please don't. You and Schneibster are making my brain do cool things. :)

[epepke]

This is also why wires with opposite currents repel, right? Because the space between the moving electrons is contracted more than the space between the more-slowly-moving protons, so the net force is a repulsive one?

Yeah, basically. The electrons see each other going twice as fast.

What's band structure?

I tried to explain it. In atoms, each electron in an orbital has a number of energy states. This is what makes neon bulbs and fluorescents work. An electron is excited, then it drops back and emits a photon.

In band structure, the individual electrons sort-of blob together in a quantum sense. This makes conduction happen, because electrons can easily flow from atom to atom. So an electron isn't limited to one orbital but occupies a "band" made of many orbitals. It also dramatically increases the number of energy states.

[Art Vandelay]

Thus, we see that magnetism is actually a relativistic effect due to the motion of the particle that is the source of the magnetic field relative to the particle that feels the force of the field.
Another way of putting it is that the electrical force is a four dimensional entity, so when we try to understand it within a three dimensional framework, often part of it gets left out. We call this part "magnetism".

The two forces have equal magnitude and opposite direction, but they don't act on the same body, so they don't cancel. They are the same magnitude, up to a translation. At any given point, the two fields will be different (except on the plane of points equidistant from the two charges).

Here is the explanation I usually give about this:

Special Relativity shows Lorentz contraction. Moving objects shorten in the direction of travel.That's not quite correct. Moving objects are observed to shorten.

[epepke]

That's not quite correct. Moving objects are observed to shorten.

Yeah, OK.

[Schneibster]

So when comoving particles are viewed from a moving frame, the total force decreases, but not by as much as the Coloumb force. The "magnetic force" is what makes up the difference. Exactly! And all of the "magnetic" effects we see are actually that "making up the difference." Isn't that very cool?

Weird.Very. And it gets more interesting- as you see below; take it and make it happen in little circles (actually, they don't move in circles- they're these little kinda 3-D rotated-butterfly- or toroid-looking patterns, and the electrons sort of "jump" from one spot in the pattern to another- but it adds up on average to a sort of revolving motion sort of thing, if you look at it mathematically) instead of a straight line. Then have it act on other ones doing the same thing, except they aren't all lined up- and it lines them up, you see, and that's where the "magnetism" comes from. 8)

Is the above the implications? :DYou got it. And you see it, judging from your reaction. There's a whole bunch of stuff in physics that works like that. You can almost think of it as "mother nature keeping her cards hid," if you get what I mean. When you start looking at quantum mechanics, and the uncertainty principle, this sort of stuff gets very cool, very quick. There is an experiment called the "delayed choice quantum eraser" that is just about the coolest, when it comes to that stuff.

Please, say more cool stuff like that.Hope this lives up to your expectations. :D

[Schneibster]

Another way of putting it is that the electrical force is a four dimensional entity, so when we try to understand it within a three dimensional framework, often part of it gets left out. We call this part "magnetism".Yep- and that whole 4-D thing is what makes relativity cool. I've been doing a lot of thinking about it, and got turned on to a very interesting way of thinking about the fact that "velocity" can be seen as a rotation about the three "not seeable" axes that result from adding t to x, y, and z- that is, rotation about x-t, y-t, and z-t planes- is another way of describing "motion," and you get the same sort of foreshortening you see when something rotates away from you in, say, the x-y plane- except you're used to seeing the foreshortening from that, but not used to seeing the foreshortening caused by the velocity. And the math is different for that foreshortening too- you use hyperbolic trig functions to calculate it rather than spherical trig, because unlike the relationships between x, y, and z, which are spherical, the relationship between t and x, y, and z is hyperbolic. So you wind up with the Lorentz transform instead of the Galilean transform you would naively expect.

[Cecil]

There is an experiment called the "delayed choice quantum eraser" that is just about the coolest, when it comes to that stuff. I've done a lot of reading about QM, double-slit experiments, Bell's Inequality, and such, but this was still mind-blowing. I googled and found this excellent description of an experiment, written for someone with conceptual but not formal understanding (like me!).

http://www.bottomlayer.com/bottom/kim-scully/kim-scully-web.htm

(rule 8).

How can the result of an experiment that's already been done change at a later date based on new incoming data? This makes my brain hurt.

[Schneibster]

Yeah, that's the one, and that's probably the best treatment of it, with the possible exception of Brian Greene's The Fabric of the Cosmos. Which, by the way, I highly recommend, along with The Elegant Universe.

[garys_2k]

Very cool that a Relativistic pseudoforce is holding my kid's pictures and school work to the refigerator door!