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The electrostatic field and potential of a supported sphere-plane electrode system placed inside a chamber are calculated from solutions of Laplace's equation using the extrapolated Liebmann method with the help of a digital computer. Calculations are made for gap/radius ratios of 1, 0.5 and 0.25, inside chambers of different sizes, and sphere-supporting rods of various dimensions up to a spherically capped cylinder. These calculations show that, in many cases, the electric field on the axis can be calculated using the analytical expression for an isolated sphere-plane system.
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Shallal et al. (1970) studied this question.
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