# How to calculate the magnetic field generated by accelerating charges?

1. Dec 14, 2013

### the_m-theorist

my guess was Jefimenko's equations could be used, am i right? also are there any other relevant equations or methods? also what does the current density derivative in the equation (in terms of the acceleration) for the magnetic field physically mean? p.s. my first post on the internet!

2. Dec 14, 2013

### Naty1

3. Dec 14, 2013

### WannabeNewton

You just use the Lienard-Wiechert potentials to get the scalar potential $\varphi$ and vector potential $\vec{A}$ and use the definitions $\vec{E} = -\vec{\nabla}\varphi - \partial_t \vec{A}$ and $\vec{B} = \vec{\nabla}\times \vec{A}$. The only hard part (and it is a really hard part) in the calculation is solving for the retarded time $t_r$ in terms of the actual time $t$ since the changes in the electromagnetic field carried by the particle have to propagate from the field point of the charge (with which $t_r$ is associated) to the observation point (with which $t$ is associated). See Griffiths chapters 10 and 11 for problem sets on this as well as on the ultra-important application to radiation fields.

EDIT: and also Heald and Marion chapters 8 and 9.

Last edited: Dec 14, 2013