Abstract
An explicit expression, , is given for the component of the electric field on the plane in the gap between two infinite, oppositely charged conducting masses bounded by the , planes and the , planes, respectively. The formula can be handled analytically and its maximum deviation from the rigorous value is one part in 5000. The coefficients of the Fourier expansion of and are given and used to write down a rapidly convergent series for the potential in the narrow gap between two right circular, coaxial conducting cylindrical electrodes. The resonant frequency of a re-entrant cylindrical cavity with a narrow gap is computed to about 0.03 percent. The radiation pattern from the open end of a rectangular wave guide terminating in an infinite conducting plane and transmitting only the mode is calculated with four-place accuracy.
DOI:https://doi.org/10.1103/RevModPhys.20.175
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