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Say you are in a fixed reference frame. Bob, is in a moving reference frame. Also, Bob has a bar magnet. If Bob were moving toward you with a magnet, would the value of the magnetic field you measure be distorted in any way by the velocity? (non-relativistic question) Or would the magnetic field you measure simply be a function of your position relative to it?

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Assuming that the magnet moving doesn't produce any emf (induced), the magnetic field won't have anything opposing it and then the field won't be distorted.

If the magnet produces emf, a current will most likely be induced. This current will set up its own $B$ which will oppose the original $B$, so the field will be distorted.

Check this out.

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  • $\begingroup$ Since my body has some electrical conductivity, and so do various metal objects in my pocket - keys, coins, dental fillings, possibly dental braces or various medical implants, possible zippers, a steel shank in the stylish hiking shoes I'm wearing for some reason, and these days possibly a phone - there will be an emf. Good call! (isn't this more than a little bit like how a hand-held metal detector works - eddy currents induced by changing magnetic fields produce new magnetic fields that are picked up?) $\endgroup$ – uhoh Jul 31 '16 at 16:36
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If you are moving at slow speeds you get $$\vec E'\approx\vec E+\vec v\times \vec B $$ and $$\vec B'\approx\vec B-\frac{1}{c^2}\vec v\times \vec E .$$

So as long as Bob doesn't see an electric field, then they see the same magnetic fields.

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