Mathematical Methods in the Physical Sciences · Problem 8.20

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · green-functions-poisson-sphere

Problem

Verify that the Green function in (8.29) is zero when r=Rr = R. Also verify that the point at which the second term becomes infinite is inside the sphere, so outside the sphere this term satisfies Laplace's equation as required. Thus write a triple integral for the solution of (8.22) for r>Rr > R which is zero on the sphere r=Rr = R.

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