ELECTRIC AND MAGNETIC FIELD PROBLEMS WITH PERIODIC CIRCULAR CYLINDRICAL SYMMETRY AND THEIR CONNECTION WITH A NOVEL GEOMETRICAL INTERPRETATION OF THE ALGEBRAIC OPERATION aN±bN

Abstract

This paper deals with the evaluation of the electric and magnetic field generated by a set of N periodically distributed filamentary conductors, in a circular arrangement. The results obtained lead to the computation of a continuous product of distances. In close connection with the computation of such a continuous product, the general problem of the factorization of a sum or difference of two powers, a N ± b N , where a and b are positive real numbers and N a positive integer, is addressed.