An Electrical Potential Analyser

Abstract

The electrical potential analyser provides, in effect, an electrical analogy to the solution of Poisson's and Laplace's equations when expressed in finite difference form. The principal object in designing the instrument was to provide an experimental alternative to the “relaxation” technique which, although invaluable in the solution of many problems, is often very lengthy and tedious. The potential analyser consists essentially of a square mesh, the nodal points of which are interconnected by low value wire resistances, and a base. Corresponding nodes on the mesh and base are connected through high value resistances. A current is applied in such a manner that an electrical potential is provided, as required, to points on the mesh and the mesh boundary; the base being either used or discarded according to the nature of the problem. Readings of potential at each mesh node are recorded by a suitable galvanometer circuit. An analyser having a square mesh, such that the mesh separation is 1/12 the side length, has been constructed and encouraging results have been obtained with its use. The instrument is easily operated and results are rapidly obtained. The use of the analyser is not limited to the solution of Poisson's and Laplace's equations. By a suitable interchange of network resistances, other equations which can be expressed in finite difference form may be solved and solutions to problems involving irregular boundaries present no undue difficulty.