Electromagnetism in Reference Frames

[Gear300]

If observer A was at rest with respect to a charge that was moving with a constant velocity |v| > 0 in observer B's reference frame, would observer A detect a magnetic field?

 

[Dale]

No. B would detect a magnetic field, A would not.

 

[Gear300]

No. B would detect a magnetic field, A would not.

I see. So, in terms of relativistic electromagnetic theory, how does that happen?

 

[Dale]

In section 6 of Einstein's original paper:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

Einstein gives the transformation laws for converting fields in one frame to fields in another frame. This follows directly from that.