= Uniformly polarized sphere
{title2=$\mathbf p=\frac{4\pi R^3}{3}\mathbf P$}
A sphere with constant <electric polarization> $\mathbf P=P\widehat{\mathbf z}$ has zero volume bound charge and surface bound <charge density> $\sigma_b=P\cos\theta$. Integrating $\mathbf r\sigma_b\,dA$ gives the displayed <electric dipole moment>. The surface distribution is purely degree one in <spherical harmonics>, so its external static <electric potential> is exactly dipolar. Its interior field is finite and is not that of a point singularity.
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