Chapter 3.3, Problem 3.22P

In Prob. 2.25, you found the potential on the axis of a uniformlycharged disk: $V\left(r,0\right)=\frac{\sigma }{2{\in }_0}\left(\sqrt{r^2+R^2}-r\right).$

(a) Use this, together with the fact that $P_l\left(1\right)=1$ , to evaluate the first three termsin the expansion (Eq. 3.72) for the potential of the disk at points off the axis,assuming $r>R$ .
(b) Find the potential for $r<R$ by the same method, using Eq. 3.66. [Note: Youmust break the interior region up into two hemispheres. above and below thedisk. Do not assume the coefficients A_l, arc the same in both hemispheres.]