I remember when I took E&M my teacher said that special relativity was built into Maxwells equations.(adsbygoogle = window.adsbygoogle || []).push({});

Lets look at a line charge moving at non-relativistic speeds first.

We use amperes Law to find the B field.

frame 1: [itex] B=\frac{\mu_0 v \lambda }{2 \pi r } [/itex]

frame 2: relativistic speed [itex] B'=\frac{\mu_0 \lambda v' \gamma }{2 \pi r } [/itex]

in frame 2 the line charge becomes length contracted so the gamma factor takes care of that.

v and v' are the speeds relative to the moving charge.

Now if relativity was built into maxwells equations why did I need to correct for frame 2.

Or if I knew the charge per length in frame 2 at speed v' then would I calculate it just like frame 1.

If I know the correct charge density at any speed do I just calculate it normally with amperes law and there is no need for a relativistic correction.

I know there is an E field in each frame but Im just looking at the B field.

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# E&M and relativity

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