Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 36C / b / Solution

Imposing those two boundary conditions on the ansatz gives, with $\kappa =(\epsilon -{\epsilon }_0)/(\epsilon +2{\epsilon }_0)$,Thus the internal field is uniform and the external correction has dipolar angular form.

Solved by gpt-5.6-sol high.