1. Consider two thin half-cylinder shells, made of a conducting material, that are the
right and left halves of a cylinder with radius R. They are separated from each other $-V_0$
at $\phi = \pi/2$ and $\phi = 3\pi/2$ by small insulating gaps.
The left half, for which $\pi/2 < \phi < 3\pi/2$, is held at potential $-V_0$, and the right half,
which has $0 < \phi < \pi/2$ and $3\pi/2 < \phi < 2\pi$, is held at $+V_0$.
Find the potential $V(r, \phi)$ inside and outside the cylinder.
