1. The problem statement, all variables and given/known data One of two nonconducting spherical shells of radius a carries a charge Q uniformly distributed over its surface, the other a charge -Q, also uniformly distributed. The spheres are brought together until they touch. What does the electric field look like, both outside and inside the shells? How much work is needed to move them far apart? 2. Relevant equations ##U = \epsilon_0 \int E_1 \cdot E_2 dv## 3. The attempt at a solution I tried using ##U = \epsilon_0 \int E_1 \cdot E_2 dv## to bash out the work it takes to move the two spheres apart to infinity but it is way too messy.