Fields in Terms of the Multipole Moments of the Source

Many if not most evaluations of electric and magnetic fields arising from source configurations are performed using multipole moments of the source distribution. As an example, Jefimenko’s equations are evaluated in the radiation zone by expansion of the charge and current distributions in their lowest order moments. The important moments, electric and magnetic dipole, and the electric quadrupole are examined in detail. The electric and magnetic fields for all regions of space relative to the source location (near, intermediate, and radiation) are evaluated using the multipole expansion of the vector potential in terms of these moments. Finally, the power radiated by the multipole moments of the source is presented.