Abstract In this Letter, the classical problem of determining the optimal shape of the pole of an electromagnet is considered. In order to determine the optimal shape, we have extended a measure theory-based method. The problem of finding the optimal shape is reduced to one consisting of minimizing a linear form over a set of positive measures. To do so, an embedding procedure is applied. The resulting problem can be approximated by a finite-dimensional linear programming problem. The solution of the problem is used to construct a nearly optimal shape. © 2008 Published by Elsevier B.V. MSC: 62K05; 28A33; 49J20; 90C05

Keywords