Find the energy stored in a uniformly charged solid sphere of radius R and charge q. Do...

Find the energy stored in a uniformly charged solid sphere of radius R and charge q. Do it three different ways:

(a) Use Eq. 2.43. You found the potential in Prob. 2.21.

(b) Use Eq. 2.45. Don’t forget to integrate over all space.

(c) Use Eq. 2.44. Take a spherical volume of radius a. What happens as a→∞?

Reference Eq. 2.43

Reference Eq. 2.45.

ReferenceEq. 2.44

Reference Prob. 2.21

Find the potential inside and outside a uniformly charged solid sphere whose radius is R and whose total charge is q. Use infinity as your reference point. Compute the gradient of V in each region, and check that it yields the correct field. Sketch V(r ).