Identities of incomplete elliptic integrals with application in electromagnetism

Abstract

In this article, a set of incomplete elliptic integrals is given to help engineering and physics students solve problems that are common in electromagnetism. First, a brief description of the elliptic integrals of the first kind and second kind is presented, followed by a list of identities of incomplete elliptic integrals involving sine and cosine functions, and finally, these identities are used to solve three physical systems: the first is the electric potential generated by a segment of a charged ring; the second is the magnetic field generated by a segment of a ring carrying a current; and the third is the magnetic field produced by an axially magnetized permanent magnet.