Time-Domain Treatment of a Spherical Boundary-Value Problem

The expressions in the time domain representing the general solution of the wave equation in spherical polar coordinates are summarized. The boundary-value problem where the tangential component of E is given as a function of time on the surface of a sphere is solved for outward-moving waves. This problem embodies the transient spherical-antenna problem as a special case. Since the solution involves solving ordinary linear differential equations with constant coefficients, it is similar to that of a transient circuit problem and Laplace transforms can be employed in a similar way.