= Spherical Neumann dipole images
{c}
{title2=$u=\Psi(\mathbf r;\mathbf r_0)+\lambda^{3/2}\Psi(\mathbf r;\lambda\mathbf r_0)+\sqrt\lambda\int_0^\lambda\Psi(\mathbf r;t\mathbf r_0)\,dt$}
For a <current dipole> in a homogeneous insulating sphere of radius $a$, let $\lambda=r^2/a^2$ and let $\Psi$ be its primary <electric potential>. The displayed representation solves the interior <Neumann boundary condition> up to an additive constant. It rewrites the spherical <Kelvin transform> correction and a distributed dipole correction using the <dipole line-integral identity>. The image parameters depend on the observation radius; this is an exact parametrized representation rather than a fixed collection of image source positions.
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