An E-Field solution for a conducting surface small or comparable to the wavelength

A new
E
-field solution is presented for the electric current and electric charge induced on a perfectly conducting surface illuminated by an incident electromagnetic field. This solution is a moment solution to the electric field integral equation on the surface. The expansion functions consist of a set of functions suitable for expanding the magnetostatic current and a set of functions whose surface divergences are suitable for expanding the electrostatic charge. The testing functions are similar to the expansion functions. With these expansion and testing functions, the new
E
-field solution works well with surfaces whose maximum dimension may be as small as
10^{-15}
wavelengths or as large as a few wavelengths. Previous
E
-field solutions begin to deteriorate when the maximum dimension of the surface falls below a few hundredths of a wavelength. The new
E
-field solution is applied to a conducting circular disk and a conducting sphere.