# Concentric charged spheres work

1. Feb 27, 2009

### EngageEngage

I have a problem that I am not sure I am working correctly.

There are 2 concentric spheres, the inner of charge -q and radius Ra and outer of charge +q and radius Rb. I am to find the work that is required to put together these two spheres in such a way.

Is it enough to find the energy stored in the electric field between them, or would this be incorrect? I guess this would be the same as the energy stored in a spherical capacitor like this.

$$\frac{\epsilon}{2}\int_{r_a}^{r_b} E^{2} d^{3}r$$

Or, do I have to find first the energy to assemble the inner sphere, and then the outer sphere, and then the work required to bring them together?

Thank you for any help.