Electric singularity near the tip of a sharp cone

The singularity of the electric fields, proportional to the radial coordinate value R/sup nu -1/, is investigated for a very sharp, perfectly conducting cone of arbitrary cross section. It is shown that, in the limit of a very small cone, the exponent nu tends to zero in proportion with the inverse of the logarithm of the maximum opening angle. Results are shown for the circular and elliptic cone, with the flat sector as a special case, and for the pyramid with n equal faces. An expression, valid for arbitrary opening angles, is presented in the case of a flat sector.<
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