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.
W=\frac{1}{2} \int \rho V d \tau (2.43)
(b) Use Eq. 2.45. Don’t forget to integrate over all space.
W=\frac{\epsilon_{0}}{2} \int E^{2} d \tau (all space). (2.45)
(c) Use Eq. 2.44. Take a spherical volume of radius a. What happens as a→∞?
W=\frac{\epsilon_{0}}{2}\left(\int\limits_{\nu }^{}{} E^{2} d \tau+\oint\limits_{S}^{}{} V E \cdot d a \right) (2.44)