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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on July 28, 2007
The Quarterly Journal of Mechanics and Applied Mathematics 2007 60(3):275-287; doi:10.1093/qjmam/hbm013
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Q. Jl Mech. Appl. Math, Vol. 60. No. 3 © The author 2007. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

On the singularity of Green's tensor for a perfectly conducting semi-infinite cone

CA Liondas and DP Chrissoulidis{dagger}

( Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece )

{dagger} < dpchriss{at}auth.gr>

Received 4 April 2006. Revise 29 January 2007.
  Abstract

This paper is intended to clarify a misunderstanding concerning the source singularity of the electric Green's tensor for a perfectly conducting semi-infinite cone of circular cross-section. Tai's series expansion of the Green's tensor is known to lack a singular term at the source region. Jones has reconstructed the solution to this problem and has pointed out the difference between his result and that of Tai. The aim of our paper is to demonstrate that, although Jones's closed-form solution is correct, there is a mistake in his comparison with Tai's series solution. We conclude that one of the two additional singular terms that Jones claims as missing from Tai's formula must be omitted. Besides, we compare Jones's closed-form solution with Smyshlyaev's solution to the very same problem. We conclude that the magnetic field expressions given by Jones and Smyshlyaev coincide, but a singular term is missing from Smyshlyaev's expression for the electric field.


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