Suppose the potential V$0($ $)$ at the surface of a sphere is specified, and there is no charge inside or outside the sphere. Show that the charge density on the sphere is given by $($ $)=02$R l$=0(2$l $+1)2$ Cl Pl$($cos $),(3\mathrm{.}88)$ where Cl $=$ $0$ V$0($ $)$Pl$($cos $)$sin d$.(3\mathrm{.}89)$