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Figure 6.5: Geometry for problem of an aperture in a perfectly conducting ground screen
illuminated by an impressed source.

By superposition, if there are volume sources within V we merely add the fields due
to these sources as computed from the potential functions.

6.3.4 The Schelkunoff equivalence principle
With Love’s equivalence principle we create an equivalent problem by replacing an
excluded region by equivalent electric and magnetic sources. These require knowledge of
both the tangential electric and magnetic fields over the bounding surface. However, the
uniqueness theorem says that only one of either the tangential electric or the tangential
magnetic fields need be specified to make the fields within V unique. Thus we may wonder
whether it is possible to formulate an equivalent problem that involves only tangential
˜
˜
E or tangential H. It is indeed possible, as shown by Schelkunoff [39, 169].
When we use the equivalent sources to form the equivalent problem, we know that they
produce a null field within the excluded region. Thus we may form a different equivalent
problem by filling the excluded region with a perfect conductor, and keeping the same
equivalent sources. The boundary conditions across S are not changed, and thus by the
uniqueness theorem the fields within V are not altered. However, the manner in which
we must compute the fields within V is changed. We can no longer use formulas for
the fields produced by sources in free space, but must use formulas for fields produced
by sources in the vicinity of a conducting body. In general this can be difficult since it
requires the formation of a new Green’s function that satisfies the boundary condition
over the conducting body (which could possess a peculiar shape). Fortunately, we showed
in § 4.10.2 that an electric source adjacent and tangential to a perfect electric conductor
˜
produces no field, hence we need not consider the equivalent electric sources (ˆ n × H)
when computing the fields in V . Thus, in our new equivalent problem we need the single
˜
tangential field −ˆ n × E. This is the Schelkunoff equivalence principle.

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