- #1
particlezoo
- 113
- 4
Consider a scenario where in one frame R, I have a magnet at rest and a solid slab of charges with an arbitrarily large mass moving at velocity v. The overall acceleration of the slab is trivial, however, the v x B exerted on the slab is divergent, thus compressive/tensile stresses are exerted on the charges within the slab.
Now, let's change the frame of reference such that we are now in the frame of reference R' of the slab. There are compressive/tensile stresses on the charges are still exerted. However, in this rest frame, the average v' is zero, therefore v' x B' = 0. This leaves us only with the electric field E'. In the prior case (frame R), we had non-zero v x B which was perpendicular to the velocity of the slab v. Therefore, in the latter case (frame R'), we would expect an electric field exerted on the slab that is perpendicular to the velocity of the magnet in frame R'. This confines the electric field to planes whose normal is parallel with said velocity. But according to theory the distant magnet should not be able to create a divergent E-field at a distance from it. So somehow the compressive/tensile stresses in the slab in frame of reference R (magnet's rest frame) which are explained by a divergent v x B would somehow have to be explained by a non-divergent E-field in frame R' (slab's rest frame).
Before I should go any further on this line of reasoning, I would like to know what your thoughts are about this. Have I already made a serious or minor mistake somewhere?
Thanks in advance.
Sincerely
Kevin M.
Now, let's change the frame of reference such that we are now in the frame of reference R' of the slab. There are compressive/tensile stresses on the charges are still exerted. However, in this rest frame, the average v' is zero, therefore v' x B' = 0. This leaves us only with the electric field E'. In the prior case (frame R), we had non-zero v x B which was perpendicular to the velocity of the slab v. Therefore, in the latter case (frame R'), we would expect an electric field exerted on the slab that is perpendicular to the velocity of the magnet in frame R'. This confines the electric field to planes whose normal is parallel with said velocity. But according to theory the distant magnet should not be able to create a divergent E-field at a distance from it. So somehow the compressive/tensile stresses in the slab in frame of reference R (magnet's rest frame) which are explained by a divergent v x B would somehow have to be explained by a non-divergent E-field in frame R' (slab's rest frame).
Before I should go any further on this line of reasoning, I would like to know what your thoughts are about this. Have I already made a serious or minor mistake somewhere?
Thanks in advance.
Sincerely
Kevin M.