Disk monopole source

The disk can be regarded as a flattened sphere oblate ellipsoid of revolution) and the needle as a stretched sphere (prolate ellipsoid of revolution). A spheroid is the same as an ellipsoid of revolution. 

Analytical solutions are possible because by letting the length of the axis of revolution tend to 0, we end up with a disk. If positioned on the surface, it is the most common of all electrode geometries. We then discover the often overlooked fact that current is not injected evenly under the surface of such a plate electrode. 

J = 1 corresponds to the current density of a spherical electrode with the same radius, 

The direction of J is perpendicular to the metal surface except at the edge, which is a singular curve where the current also leaves the edge in directions of the tissue surface. Current density therefore diverges at the edge. The edge is therefore outside the zone of linearity. There are many misconceptions in the literature, with current density under a surface electrode considered uniform. The current density in the disk center is the same as on the surface of a sphere of the same radius a. The potential field in the tissue is  

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