 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-4/36c/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Imposing those two boundary conditions on the ansatz gives, with

κ = (ε - ε_{0}) / (ε + 2 ε_{0})

α = \frac{3 ε _{0}}{ε + 2 ε _{0}}, β = 3 a^{3} κ, δ = - a^{3} κ .

Thus the internal field is uniform and the external correction has dipolar angular form.

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