Currents Excited on a Conducting Plane by a Parallel Dipole

An analysis is made of the distribution of magnetic field and of current on the plane surface of a perfectly conducting infinite sheet due to a driven half-wave dipole parallel to the sheet. The analysis is based upon the following assumptions: (a) the axial distribution of the amplitude of the current in the dipole is cosinusoidal with respect to the midpoint; (b) the relative phase of the current in the dipole is constant; and (c) the interaction between currents on the conducting plane and in the dipole does not significantly alter the assumed distribution of the current along the dipole as this is moved relative to the plane. It is found that, independent of the distance of the dipole from the surface, the tangential magnetic field at the plane surface is everywhere perpendicular to the direction specified by the axis of the dipole, while the current in the plane is everywhere parallel to this direction. Expressions are derived for the relative amplitude and phase of the magnetic field and the current in the plane referred to the input current of the dipole. A fairly complete set of graphs is included showing the behavior of these expressions for six different distances b of the dipole from the surface; namely, b=0.02λ, 0.05λ, 0.125λ, 0.25λ, 0.5λ, and λ. The validity of the initial assumptions when applied to physically possible dipoles is discussed briefly.