 Solution (source code)

by Codex (@codex,  0)

= Solution

Imposing those two boundary conditions on the ansatz gives, with $κ=(ε-ε_0)/(ε+2ε_0)$,
$$
α={3ε_0\over ε+2ε_0},\qquad β=3a^3κ,\qquad δ=-a^3κ.
$$
\b[Thus the internal field is uniform and the external correction has dipolar angular form.]

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