Electric and magnetic fields from a semi-infinite antenna above a conducting plane

The electric and magnetic field structures around a semi-infinite thin-wire antenna vertically placed above a perfectly conducting ground plane are investigated when the antenna is supporting two different types of sources. It is shown that when the wire is carrying a uniform line charge, the electrostatic potentials are equal on the surfaces of imaginary cones of fixed cone angles with axis along the wire and apex at the conducting plane. The electrostatic field vectors are shown to be perpendicular to the imaginary cones and tangential to the meridian lines of half-spherical shells centered at the base of the line charge. The vertical components of the electrostatic field on the surface of these imaginary half-spherical shells of a given radius are constant, except at the wire itself. The magnetic field structure associated with a constant current in the semi-infinite antenna is that of an infinite wire. The electric and magnetic fields due to a time-varying charge or current pulse propagating with the speed of light along the vertical thin-wire antenna have a spherical transverse electromagnetic (TEM) field structure, identical to that for the case of a uniform line charge and a uniform current. The connection between the static and dynamic solutions is derived mathematically using two different approaches.