A point dipole p oriented along the z-axis is placed at the center of a spherical cavity of radius R with conducting walls. The walls are grounded.

Find the potential everywhere inside the cavity using the general solution in spherical coordinates,

V(r, theta) = Sigma [A_lr^l + B_l/r^l + 1](cos theta),

with the following two boundary conditions:

V = 0 at r = R and (ii) V rightarrow V_dipole as r rightarrow 0.