Electric singularity near the tip of a sharp cone

The singularity of the electric fields, proportional to the radial coordinate value R^ν-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 ν 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