The electric potential in the region of a thin slit

In the course of determining the potentials within a mass spectrometer source, simple rules have been discovered which aid the calculation of potentials about a thin slit. These rules, of which there are four, make possible the approximation with ruler and compass of the equipotentials formed by opening a long, narrow slit in a thin conductor separating regions of uniform electric field. A simple iteration formula is included which enables the approximate potential at any point to be refined to any desired degree. Proofs of these rules are developed with the aid of conformal mapping in the complex plane.