Abstract
AbstractThis paper considers the problem of expressing the magnetic scalar potential associated with the steady flow of an electric current around a thin circular wire, in terms of ‘local’ toroidal coordinates. This potential is known to be a multi-valued function of position and so cannot be expressed directly in terms of fundamental (i.e. single-valued) solutions of Laplace's equation. It is shown that the potential can however be expressed quite simply, as an infinite series of multi-valued toroidal harmonics and that this series is rapidly convergent in the neighbourhood of the current-ring.
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