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Derivation of the Electric Field Operator Equation

Let denote the surface of a perfectly conducting scatterer with unit normal vector . may be either open or closed. The incident electric field is due to an impressed source in the absence of the scatterer. The boundary condition is such that the sum of the incident, , and the scattered, , electric fields has no tangential component on the perfectly conducting body surface, i.e.,

where the subscript ``tan" denotes the components tangential to the surface . is the electric current which is induced on the surface due to the incident field. If is open, we regard as the vector sum of the currents on opposite sides of .

The scattered electric field can be represented by the so-called vector potential and the scalar potential which are produced by the surface current, as below:

The magnetic vector potential, , and the electric scalar potential are given by [47]:

An time dependence is assumed and is suppressed, and , where is the wavelength. The permeability and permittivity of the surrounding medium are and , respectively, and and are the arbitrarily located observation point and source point, respectively. The surface charge density is related to the surface divergence of through the equation of continuity,

where is the surface divergence operator. Substituting () into eq (), an integro-differential equation for is given by

With and given by eqs () and (), () is the so-called electric field integral equation (EFIE). In the next subsection, the method of moments is applied to obtain a matrix equation for the unknown surface current.



Next: Numerical Formulation for Up: Electric Field Integral Previous: Electric Field Integral


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Sat Dec 3 17:51:03 EST 1994