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.

 

[sardar]

Yes, observer A would detect a magnetic field. This is because according to the theory of electromagnetism, a moving charge produces a magnetic field. In this scenario, the charge is moving with a constant velocity in observer B's reference frame, which means it is accelerating in observer A's reference frame. This acceleration of the charge in observer A's frame creates a changing electric field, which in turn produces a magnetic field. Therefore, observer A would detect a magnetic field due to the moving charge.