$($Actually this is more like a chapter $2$ problem, problem $3\mathrm{.}9$ and $3\mathrm{.}10$ of chapter $3$ are better as there the range is limited in the z$-$direction$)$ Consider an infinite long hollow cylinder with radius a as shown in the figure below. The cylinder's cylindrical surface $(r=a)$ is kept at and electric potential $V_{o}sin(f).$ Assume that there is no charge in the cylinder, i$.$e$.$ the space in the cylinder $rfr=a{V}_{o}sin(f)r=00$ :$-1$ and $1$ for $0$ :