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• W1522247078 abstract "The classical treatment of the Laplace equation by separation of variables in bispherical coordinates is used to obtain analytical expressions and numerical results for the solution of various electrostatic problems for a perfectly conducting spindle: charged spindle in free space, spindle in a uniform axial or transverse electric field. Special attention is paid to the limit case of a spindle passing into a tight torus, that is a torus without central hole. It is shown that in this limit case the solutions of the potential problems for a spindle tend continuously to the corresponding solutions for a tight torus, as obtained by Belevitch and Boersma. In addition, approximations to the capacity and to the induced dipole moments are derived for the case of a spindle that is almost a tight torus. Math. Rev.: 78A30, 33A45, 33A40 1. Introduetion In a recent paper 1) Belevitch and Boersma treated some electrostatic problems for a perfectly conducting torus: charged torus in free space, torus in a uniform axial or transverse electric field. The solutions of these potential problems were derived by separation of variables applied to the Laplace equation in toroidal coordinates. For the limit case of a tight torus, that is a torus without central hole, the solutions of the mentioned problems were obtained by use of Kelvin' s inversion. Next it was shown that the solutions of the potential problems for the tight torus coincide with the limits of the solutions for the general torus when the radius of the central hole tends to zero. In this paper we consider the same electrostatic problems for a perfectly conducting spindle. The spindle is a surface of revolution that is generated by rotating a circular are around its supporting chord. Both the spindle and the torus can be described by two parameters a, b, where a isthe radius of the circular cross-section with a plane through the revolution axis, and b is the signed distance of the cross-section center to the revolution axis of the spindle or torus. The parameters a, b are restricted by - a a for the torus. The tight torus is described by equal radii a = b, and is therefore limit case of both the torus and the spindle." @default.
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• W1522247078 date "1984-01-01" @default.
• W1522247078 modified "2023-09-25" @default.
• W1522247078 title "SOME ELECTROSTATIC PROBLEMS FOR A SPINDLE" @default.
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