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A radial current dipole has moment parallel to its displacement from the sphere centre. The Sarvas formula gives identically zero exterior magnetic field for such a source in a spherical volume conductor model, although its electric potential need not vanish. This is a nonuniqueness mechanism for the inverse problem in magnetoencephalography.

For the exterior of a spherical volume conductor model, put $P=|\mathbf{r}-{\mathbf{r}}_0|$, $r=|\mathbf{r}|$ and $F=r{P}^2+P\mathbf{r}\cdot (\mathbf{r}-{\mathbf{r}}_0)$. The displayed Sarvas formula follows by taking the radial component of the Geselowitz formula and integrating the magnetic scalar potential from infinity. It is independent of a spherically symmetric conductivity profile. The sign shown uses $\mathbf{B}=+{\mu }_0\nabla U/(4\pi )$; conventions defining a magnetic potential with a minus sign reverse $U$. Sarvas's original paper derives the spherical-conductor field and its consequences for the inverse problem.

A spherical volume conductor model approximates a conducting body by a sphere, usually with uniform or radially stratified conductivity. It provides explicit forward models for electroencephalography and magnetoencephalography. Its symmetry makes a radial current dipole magnetically silent outside the sphere; departures from spherical symmetry need not retain that property.