An approximate solution of Laplace's equation is used to determine the potential distribution in a current-carrying cylinder containing a circular constriction along its axis. Although the expression for the potential was derived for the case when the radius b of the constriction is small in comparison with the radius a of the cylinder, the results have been found to represent a good approximation to the exact solution for values of b/a approaching 0.5.
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R. S. Timsit (1977) studied this question.
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