Geselowitz formula ($\mathbf{B}={\mathbf{B}}^p-\frac{{\mu }_0\sigma }{4\pi }{\int }_{S}u{\mathbf{n}}^{\prime }\times \frac{\mathbf{r}-{\mathbf{r}}^{\prime }}{|\mathbf{r}-{\mathbf{r}}^{\prime }{|}^3}d{S}^{\prime }$)

For a homogeneous volume conductor with an insulating boundary $S$, the Geselowitz formula expresses the exterior magnetic field as the primary Biot-Savart law field minus a surface contribution from the induced electric potential. For a current dipole, ${\mathbf{B}}^p={\mu }_0\mathbf{Q}\times (\mathbf{r}-{\mathbf{r}}_0)/(4\pi |\mathbf{r}-{\mathbf{r}}_0{|}^3)$. On a spherical boundary, ${\mathbf{n}}^{\prime }$ is parallel to ${\mathbf{r}}^{\prime }$, so the surface term has zero radial component at the observation point.