Prove that the potential \(\phi(0)\) at the center of a charge-free spherical volume \(V\) is the equal to average of \(\phi(r)\) over the surface \(S\) of the sphere. Using
- Green’s reciprocity relation.
- Green's identity\[\iiint d^3r (f \nabla^2 g − g\nabla^2 f ) = \iint \hat{n} · (f \nabla g − g\nabla f) dS\]
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