I have heard about how magnetic fields can be explained as electric fields that arise from length dilation of moving charges in a conductor. Intially this seemed convincing but there are two things that dont seem to make any sense to me:
- Why isnt there a force on a stationary test charge next to a current carrying conductor? The charge of the conductor needs to be neutral when no current is flowing. But if current is flowing the electrons move and should be relativistically dilated, while the nuclei remain stationary. This should result in an apparent negative charge from a stationary observer, hence a force on the test charge.
- Why is there a magnetic force on test charges moving perpendicular to the conductor, as described by the Lorentz Force? If the test charge is moving perpendicular to the conductor there should be no length contraction at all in the conductor and therefore no effect at all.
