Magnetic field of charge moving at constant velocity

[jtbell]

In the case of a uniformly moving charge you get the fields also from Lorentz boosting the Coulomb field for the charge at rest.

Sorry to be a bore about this point, but can anybody demonstrate that?

See here:

http://farside.ph.utexas.edu/teaching/em/lectures/node125.html

(two methods, take your choice)

 

[Per Oni]

Jtbell that paper your referring to doesn’t look like “ a Lorentz boosted coulomb field” to me. It looks a lot more complicated including a lot of maths and Greek. Oh well, someday someone will come up with something a bit more consumer friendly.

 

[vanhees71]

I find the manuscript by Fitzpatrick excellent. It's also awailable as a textbook. I can only recommend to read his chapter on the fully relativistic treatment of electromagnetics. I never understood, why there is no textbook on classical electromagnetism that from the very beginning strictly uses the relativistic framework. Instead all authors copy more or less the classical textbooks of the first half of the 20th century (although there are excellent books among them, first of all Sommerfeld's Lectures on Theoretical Physics and Becker's book). The only exception is Landau-Lifgarbages in his vol. II, but in vol. VIII he treats the constitutive equations non-relativistic as usual. But that lamento becomes off-topic now...

 

[Dale]

Jtbell that paper your referring to doesn’t look like “ a Lorentz boosted coulomb field” to me.

But that is exactly what it is.

 

[Shaw1950]

Thank you all for the comments and feedback it was most helpful and has spurred me on to do some of the maths for myself. One of my difficulties is that many textbooks "fudge" the solution by ignoring the fact that a point charge is essentially a delta distribution and they skip essential steps in the calculation. However, you all encouraged me to make the effort, after 40 years of abstinence. Thanks!