I remember when I took E&M my teacher said that special relativity was built into Maxwells equations.
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.
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.
