Image Theory for an Arbitrary Quasi-Static Field in the Presence of a Conducting Half Space


  • J. T. Weaver


The approximate image theory for quasi-static fields in the presence of a conducting half space is treated in full generality by considering an arbitrary periodic source. The general theory is developed in terms of a magnetic Hertz vector aligned perpendicular to the plane surface of the conductor. It is shown that its solution above the conductor can be expressed as the combined Hertz potentials of the source and its image located at a certain complex depth, plus terms that become negligibly small for points somewhat farther than a skin depth from the ordinary mirror image of the source. Image approximations for the individual electric and magnetic field components are derived. The magnetic field is expressed entirely in terms of the magnetic field of the source and its complex image, but the electric field, unless it is everywhere parallel to the surface of the conductor, depends in addition on the mirror image of the source. The general theory is illustrated by its application to the particular examples of magnetic dipole and infinite line current sources.