Radiation of electromagnetic waves by a time-harmonic surface charge density

The radiation process of waves by a time-harmonic electric charge density, located on the surface of a conducting sphere, is investigated. The current density is evaluated using the continuity equation. The scalar and vector potential are obtained by using the integral solution of the inhomogeneous Helmholtz equation. The radiated electric and magnetic fields are derived. The effect of the ground is put forth. The behaviors of the waves are studied numerically.