(i) Two point charges, of opposite sign and unequal magnitude, are placed at two different locations. Show that the combined electrostatic potential vanishes on a sphere that encloses only the charge of smaller magnitude.

(ii) A grounded, conducting sphere of radius $a$ is centred at the origin. A point charge $q$ is located outside the sphere at position vector $\mathbf{p}$. Formulate the differential equation and boundary conditions for the electrostatic potential outside the sphere. Using the result of part (i) or otherwise, show that the electric field outside the sphere is identical to that generated (in the absence of any conductors) by the point charge $q$ and an image charge $q^{\prime}$ located inside the sphere at position vector $\mathbf{p}^{\prime}$, provided that $\mathbf{p}^{\prime}$ and $q^{\prime}$ are chosen correctly.

Calculate the magnitude and direction of the force experienced by the charge $q$.