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Bioelectromagnetism studies electric fields, electric currents and magnetic fields associated with living systems and their interaction with applied fields. Ionic currents across and along biological cell membranes generate measurable signals; the surrounding tissue conducts and redistributes them.

In electrocardiography, surface electrodes measure electric potential differences produced by distributed cardiac activity rather than directly recording one isolated cell. A volume conductor model relates internal source currents to those surface readings. Electrode position and conducting geometry matter, so a changed voltage can reflect source activity, measurement contact or the current paths through tissue.

A current dipole idealizes a localized impressed electric current density by the displayed Dirac delta function distribution. Its moment $\mathbf{Q}$ has units of current times length. In a homogeneous volume conductor of conductivity $\sigma$, its primary electric potential is $\Psi (\mathbf{r};{\mathbf{r}}_0)=\mathbf{Q}\cdot (\mathbf{r}-{\mathbf{r}}_0)/(4\pi \sigma |\mathbf{r}-{\mathbf{r}}_0{|}^3)$.

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.

A volume conductor is a conducting three-dimensional medium through which electric currents flow. In the quasistatic bioelectric model, the total current density is $\mathbf{J}={\mathbf{J}}^p-\sigma \nabla u$, comprising an impressed source current and its Ohmic return current. Electric charge conservation gives $\nabla \cdot (\sigma \nabla u)=\nabla \cdot {\mathbf{J}}^p$. An insulating boundary has zero normal total current.