A formulation of the integro-differential equation for the electric field (or equivalent surface magnetic current) in a finite-length narrow slot in a perfectly conducting planar screen of infinite extent is presented. An analogous developement leads to the dual equation for a finite-length narrow conducting strip. The derivation proceeds from the general aperture equation and incorporates the known field in a narrow slot of infinite extent. The formulation is not based upon the concept of an equivalent radius but, as a by-product, width/4 emerges as the value of the equivalent radius of a strip or a slot.
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C.M. Butler (1982) studied this question.
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