Why does current produce magnetic field (in a deeper sense)

[CyberShot]

I know it's described by Biot-Savart and it's because the charges are moving.

But, instead of taking it for a given, has anyone asked the question: why does the magnetic field wrap around the current? In essence, why is there a physical separation of current and B field? And why is it specifically a circular wrapping, why not square? Or triangular?

Do the moving charges "spit" out a magnetic field which then wraps around the charges themselves? Doesn't this violate locality? The spat out magnetic field must travel a certain distance to wrap around the current.

The magnetic field somehow is created at an arbitrary distance away from the current. How can something be created at a distance from something else? Doesn't there have to be a "physical" line of connection between the current and B field? Does physics have an answer?

 

[RedX]

I know it's described by Biot-Savart and it's because the charges are moving.

But, instead of taking it for a given, has anyone asked the question: why does the magnetic field wrap around the current? In essence, why is there a physical separation of current and B field? And why is it specifically a circular wrapping, why not square? Or triangular?

Do the moving charges "spit" out a magnetic field which then wraps around the charges themselves? Doesn't this violate locality? The spat out magnetic field must travel a certain distance to wrap around the current.

The magnetic field somehow is created at an arbitrary distance away from the current. How can something be created at a distance from something else? Doesn't there have to be a "physical" line of connection between the current and B field? Does physics have an answer?

The magnetic field has to be cylindrically symmetric in magnitude, so a triangle or square is out of the question. As for why it's in the plane perpendicular to the wire, I can't think of an obvious answer.

In any case, you can derive all of magnetism from electricity. Say you have an electric charge just sitting there. If you go into another frame of reference, the charge is moving so that it becomes a current. So you should be able to derive the result that the magnetic field encircles the current in a plane perpendicular to the current.

As for locality, the Green's functions in classical electrodynamics are local (although this is not so in quantum theory). So all fields propagate at the speed of light from sources like Huygen wavelets.

 

[CyberShot]

The magnetic field has to be cylindrically symmetric in magnitude, so a triangle or square is out of the question. As for why it's in the plane perpendicular to the wire, I can't think of an obvious answer.

In any case, you can derive all of magnetism from electricity. Say you have an electric charge just sitting there. If you go into another frame of reference, the charge is moving so that it becomes a current. So you should be able to derive the result that the magnetic field encircles the current in a plane perpendicular to the current.

As for locality, the Green's functions in classical electrodynamics are local (although this is not so in quantum theory). So all fields propagate at the speed of light from sources like Huygen wavelets.

So, let's say we were traveling alongside the charges at the same speed as those charges in the current, at some v < c (say 2/3c). Relativity allows this. In our reference frame, the charges would just be sitting there, thus not moving. Does this mean that we would not see a magnetic field produced in our reference frame?

If so, relative to a stationary observer, a magnetic field would be seen. Wouldn't this mean that a B field would occur and not occur? Is there no absolute world-sheet frame that has the "right" answer?

 

[Drakkith]

See here: http://en.wikipedia.org/wiki/Relativistic_electromagnetism

So, let's say we were traveling alongside the charges at the same speed as those charges in the current, at some v < c (say 2/3c). Relativity allows this. In our reference frame, the charges would just be sitting there, thus not moving. Does this mean that we would not see a magnetic field produced in our reference frame?

If so, relative to a stationary observer, a magnetic field would be seen. Wouldn't this mean that a B field would occur and not occur? Is there no absolute world-sheet frame that has the "right" answer?

If you AND a charge were traveling parallel to each other with the same velocity you would NOT see a magnetic field. Now imagine that instead of a single charge you have a long wire with current moving through it in the direction you are traveling. (When I say current moving through it I mean electrons moving, not positive charges like standard electronics uses)

So, a current is moving with you at the same speed, what do we see? From OUR frame of reference it looks like the electrons aren't moving and that it is the positive charges that are moving. Since they are moving they are length contracted and the distance between each charge is reduced, IE they are closer together. So from our frame we have a conductor with MORE positive charges than negative charges per area. This means that to us there is a POSITIVE charge on the wire, AKA a magnetic field. If you reversed the direction of the current the negative charges would be traveling at 2x the speed of the positive charges from our frame, meaning that they are MORE length contracted and closer together than the positive charges, resulting in a NEGATIVE charge on the wire, AKA a magnetic field of the opposite pole. Exactly what happens when you switch the direction of a current in an electromagnet.

That is pretty much the basics of that article. I don't know how this applies to a single particle and its intrinsic spin though.

 

[Evil Bunny]

Wow, I never even thought about relativity in electricity. Thanks Drakkith for posting that! Very interesting...

 

[CyberShot]

Since a satisfactory answer was not given, I will repeat the following question.

Relative to a stationary observer, a magnetic field would be seen, but relative to an observer riding on a charge it would not. Wouldn't this mean that a B field would occur and not occur? Is there no absolute "space-time fabric" frame that has the "right" answer?

 

[Drakkith]

Since a satisfactory answer was not given, I will repeat the following question.

Relative to a stationary observer, a magnetic field would be seen, but relative to an observer riding on a charge it would not. Wouldn't this mean that a B field would occur and not occur? Is there no absolute "space-time fabric" frame that has the "right" answer?

First, no, there is no absolute frame that is correct. Every frame is correct.

Second, if you were riding along with a charge in space you would only see the electric field, not a magnetic one.

 

[BruceW]

The Biot-Savart law is derived from Maxwell's equations, using the mathematical properties of vector fields.
So Maxwell's equations are the deeper meaning.
Also Drakkith is right, the laws are the same in all frames, and the B field is not the same in all frames.
Kinetic energy of the particle is also different, depending on the frame you view it from.