**Problem**

Find the potential between two concentric conducting spheres or radius and . The potential at is and the potential at is .

**Solution**

This problem is a Laplace equation problem in one dimension and in the spherical polar coordinates.

Integrating twice yields the

At

At

Solve for the constants and in a system of simultaneous equations.

So the solution for the potential is

- .

Community content is available under CC-BY-SA unless otherwise noted.