# Electrodynamics thought experiment

1. Aug 25, 2011

### soothsayer

So I was thinking about E&M today, and specifically, how E&M relates to the ideas of relativity. Specifically, that magnetism is induced by a change in an electric field and vice versa. This got me thinking of some scenarios. In each, you have a particle emitting a constant magnetic field and another emitting a constant electric field.

In the first scenario, you have one particle stationary at one point. The second particle is at some radius from it. A centripetal force is applied on the second particle which induces circular movement. The particles now "see" each other moving, and their respective fields changing, and the two particles begin to exert a force on each other.

This is all correct, right? I've only taken freshman level E/M courses really, which is why I could use some help.

The second scenario is a bit trickier. The two particles are at the same position on a rotating plate. From an outsider's perspective, the second particle seems to be rotating around the first particle, which is stationary but spinning in the center of the disk. The observer notices, for example, if the rotating particle is electrically charged, that it begins to create a magnetic field due to the changing electric field. However, the particles are not attracted to each other because, all though there is circular motion of one, the other particle is in the exact same reference frame and does not "see" any movement from the other particle.

The third scenario involves the first particle at the center of our rotating disk and the second particle just outside of it. An outside observer sees no movement of either particle besides the rotation of particle one. The observer measures no INDUCED electric or magnetic fields. However, the first particle "sees" the second particle rotating around it, as a person on a rotating disk might see a person outside of it and perceives an induced field. There is now a force between them which the observer obviously sees and interprets as a mysterious force.

Are any of these right? Or do I have a fundamental misunderstanding of this idea in E/M? I could use some help/refining.

2. Aug 26, 2011

### Drakkith

Staff Emeritus
I think that is mostly correct. However remember that the electric field from each particle would cause them to interact even when the magnetic field isn't there, and will be attracted or repelled accordingly.

3. Aug 26, 2011

### soothsayer

Drakkith, what about if one particle had a charge, and an electric field, but the other was magnetized, like a ferromagnet? Would they still attract each other if both at rest?

4. Aug 26, 2011

### Drakkith

Staff Emeritus
Umm, I don't think so. I think a charged particle has to be moving or has to have a changing magnetic field to cause interaction. The intrinsic angular momentum possessed by charged particles causes it to have a constant magnetic field, however when stationary I think the particle simply orients its field either with or against the magnets field. Look up the Lorentz Force for more.

5. Aug 26, 2011

### atyy

Classically, a "particle" that produces a magnetic field without an electric field is best thought of as a small loop of current.

Maxwell's equations in their standard form hold only for frames moving at constant velocity (Lorentz inertial frames).

A particle that is accelerating with respect to an inertial frame (eg. one that is undergoing circular motion) will radiate electromagnetic waves.