A new type of expansion in radiation problems

Abstract

A new type of expansion of i(1)eikr12r12 is developed. Here i is a vector function of the spherical coordinates denoted by 1 and r12 is the distance between two points denoted by 1 and 2. This expansion is used in the solution of Maxwell's equations and a simple general expression is found for the energy radiated from a known current distribution. A brief application to Dirac's theory of radiation is given. An expansion for i(1)r12 is developed which can be used to find the vector potential due to a steady current distribution. © 1935 The American Physical Society.