Eddy-current modes in linear solid-iron bars

The solution of Maxwell´s equations to find the magnetic-field decay in a long rectangular iron bar of constant permeability is a classical problem in electromagnetic theory, with a well known solution. The converse problem of establishing the field when a voltage is applied to a winding on the bar is much more difficult, and has not been satisfactorily solved. Re-examination shows that the orthogonality of terms in the classical series solution leads to an exact circuit representation of the solid iron, composed of an infinite number of network loops. The explicit solution is found to be readily available by numerical methods using a digital computer, since the networks may be described by rapidly converging infinite series. Computed results are compared with answers obtained analytically by considering only a very few of the network loops. In determining time constants, accuracies of the order of within 1% are shown to be achievable, using a simple network analysis without the use of computing machines. Formulas for calculating the necessary network-component values, together with some sample computer results, are given.