Calculation of inductance and capacitance by means of dual energy principles

Abstract
The sources of a magnetic field can be regarded as either electric currents or magnetic poles. This makes it possible to describe the field energy as kinetic or potential and to write the field equations in terms of two alternative Lagrangian densities. These two Lagrangians have the property that they provide lower and upper bounds to the field energy. The existence of dual bounds enables accurate approximations to be made in a very simple manner. Nonlinear fields can be treated by the method, and so can 3-dimensional problems. The method is also applicable to electric fields. Examples are given in the paper.