A moving magnet in a linear electric field

[GregM]

If a electrically charged mass travels thru a magnetic(m) field, it will accelerate at right angles to its velocity and the m-field. Under some conditions like this the charged mass will travel in a circular loop due to this magnetic force acceleration. This info is all over the internet. e.g.
https://courses.lumenlearning.com/b...on-of-a-charged-particle-in-a-magnetic-field/

What about a moving magnet in an electric field? A similar effect? Seems not a word has ever been written about it. Google returns nothing. Perhaps no-one has ever thought to do this experiment. Potential for a ground breaking 19th century style experiment here. Which one of us will be the neo Faraday? I wonder what the Heaviside equations predict.

 

[GregM]

problem with the heaviside equations is they associate electric charge with mass, but not magnetic charge. Its harder to see how magnetic mass experiences force.

 

[vanhees71]

https://link.springer.com/article/10.1140/epjp/i2014-14215-y
https://iopscience.iop.org/article/10.1088/0143-0807/32/4/003/meta
https://iopscience.iop.org/article/10.1088/0143-0807/33/1/L02
https://iopscience.iop.org/article/10.1088/0143-0807/33/1/L03/meta

As you see, it's not an easy topic, and there seems to be some debate about it. I've not thought about it myself. So I can't make any statement about it yet.

 

[GregM]

can't they just report the results of dropping a bar magnet between 2 large long capacitor plates? Debate about interpretation of the results should come later.

 

[Meir Achuz]

https://link.springer.com/article/10.1140/epjp/i2014-14215-y
https://iopscience.iop.org/article/10.1088/0143-0807/32/4/003/meta
https://iopscience.iop.org/article/10.1088/0143-0807/33/1/L02
https://iopscience.iop.org/article/10.1088/0143-0807/33/1/L03/meta

Those papers contradict each other because they're all wrong. A magnetic would require an inhomogeneous magnetic field to feel a force. There are some papers claiming that a moving magnet acquires an electric dipole moment, but they are also wrong.

 

[vanhees71]

But the latter is correct. If you have a permanent magnet and view it from an inertial frame, where it's moving there's also an elecctric dipole moment. It's because the electric and magnetic polarizations of a medium are components of an antisymmetric 2nd-rank Minkowski tensor in a similar way as the electric and the magnetic field are components of such an antisymmetric tensor. The only difference is that due to the historical misconception of magnetization there's a sign change. So you have
$$F^{0j}=-F^{j0}=-E^j, \quad F^{jk}=-\epsilon^{jkl} B^l$$
and
$$P^{0j}=-P^{j0}=p^j, \quad P^{jk}=+\epsilon^{jkl} m^l,$$
where ##\vec{E}## are the electric, ##\vec{B}## the magnetic field components and ##\vec{p}## the electric and ##\vec{m}## the magnetic polarization of the matter.

Thus an uncharged permanent magnet which has only a magnetization in its rest frame has both an electric polarization and a magnetization in any other inertial frame.

 

[Meir Achuz]

"the electric and magnetic polarizations of a medium are components of an antisymmetric 2nd-rank Minkowski tensor"
There's no proof of that for a permanent magnet.

 

[vanhees71]

That's standard relativistic electrodynamics.

 

[Meir Achuz]

I didn't realize that was the proof.