Concentric charged spheres work

[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.

 

[NateD]

The correct approach is to find the energy stored in the electric field between them. The energy stored in a spherical capacitor like this can be found using the equation that you provided: $\frac{\epsilon}{2}\int_{r_a}^{r_b} E^{2} d^{3}r$. This equation takes into account both the energy required to assemble the inner and outer spheres, as well as the work required to bring them together.