Fig 1. Current source: A current in an homogenous medium yields a current source density flowing in all directions.

The current density writes: ${\displaystyle \overrightarrow{J}=\frac{I{\overrightarrow{u}}_r}{4\pi r^2}}$, where r is the distance to the current source and I the current generated at the origin. The Ohm law ($\overrightarrow{J}=\sigma \overrightarrow{E}$) leads to the potential ${\displaystyle V=\frac{I}{4\pi \sigma r}}$ created at any distance r.