Calculating Angular Momentum of a Monopole-Charge System

[XieJiaLin]

A magnetic monopole, if it existed, would produce a magnetic field B = gr/r^3, where g is the magnetic charge, and r is the distance from the monopole. Calculate the angular momentum of a system consisting of a monopole g and a charge e, both at rest.


The attempt at a solution

I know that the angular momentum points from the charge to the monopole with a magnitude of ge/c; however, I'm not sure how to show this. Any help starting out would be greatly appreciated.

 

[arkajad]

Probably you mean generalized angular momentum. Perhaps you need to take into account the electric field of the charge and the magnetic field of the monopole and calculate

$$\frac{1}{4\pi}\int\,d^3r'[\mathbf{r}'\times(\mathbf{E}\times\mathbf{B})]$$

using the facts that $$\mathbf{B}(\mathbf{r}')=-g\nabla\frac{1}{r'}$$

and

$$(\nabla'\cdot \mathbf{E})=4\pi e\delta^3(\mathbf{r}-\mathbf{r}')$$

where $$\mathbf{r}$$ is the position of the charge. Integration by parts may be useful.