Radiating Systems, Multipole Fields and Radiation — John David Jackson
Physics — E&M · spherical-shell-radiation
Problem
Two halves of a spherical metallic shell of radius R and infinite conductivity are separated by a very small insulating gap. An alternating potential is applied between the two halves of the sphere so that the potentials are ±Vcosωt. In the long-wavelength limit, find the radiation fields, the angular distribution of radiated power, and the total radiated power from the sphere.