Electromagnetic Boundary Problems

7.4    INTEGRAL EQUATIONS FOR STATIC “SCATTERING” BY CONDUCTORS

In this section we will again consider the geometry of Section 7.2, but now with a static field “incident” upon the scatterer (i.e., the incident field is what would be produced by the impressed sources in the absence of the conductor S)⁸ In the static limit, the electric and magnetic problems decouple, and we consider them separately (see Section E.2).

7.4.1    ELECTROSTATIC SCATTERING

Let a static incident electric field Eⁱ(r) = −∇Φⁱ(r) be characterized by means of a potential Φⁱ(r), which is the result of some static charge distribution ρ_ext(r) located external to S. When a perfect conductor⁹ whose surface is S is introduced into this incident field, a redistribution of ...