Electromagnetic Force in Special Relativity

[L0r3n20]

Hi! I came out with a problem last night I wasn't able to solve:

Let's assume we have a condensator with a uniform electric field E confined in its inside, lying on the z axes. Let's also assume we have a piece of a ferromagnetic object aligned with the condensator at time t = 0, on the y-axes. We now perform a boost along the x-axes for both the object: we will find the electric field shifted by a gamma factor and a new magnetic field along the y-axes. So, in the moving frame, the ferromagnetic object would now feel a force toward the condensator.
I cannot understand how this is possible being the Lorentz transformation a switch among inetrial frames.

 

[Dale]

Don't forget to transform the ferromagnetic object too!

 

[L0r3n20]

Do I have to transform every magnetic domain? Aren't they negligible?

 

[Orodruin]

Do I have to transform every magnetic domain? Aren't they negligible?

The force on an object depends on the internal charges and currents. Not only on the EM field. Charge and current densities also need to be properly transformed.

 

[Dale]

Do I have to transform every magnetic domain? Aren't they negligible?

Clearly they are not negligible in this problem.

The electric field and the magnetic field are components of the electromagnetic field tensor, so what is purely an electric field in one frame becomes both an electric and a magnetic field in another frame. Similarly the magnetization and polarization are components of the magnetization-polarization tensor, so what is purely magnetization in one frame becomes both magnetization and polarization in another frame.