Electric singularity near the tip of a sharp cone
Abstract
The singularity of the electric fields, proportional to the radial coordinate valve R exp nu1, 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.
 Publication:

IEEE Transactions on Antennas and Propagation
 Pub Date:
 January 1988
 DOI:
 10.1109/8.1089
 Bibcode:
 1988ITAP...36..152D
 Keywords:

 Cones;
 Electromagnetic Fields;
 Polyhedrons;
 Singularity (Mathematics);
 Tips;
 Legendre Functions;
 Spherical Coordinates;
 Electronics and Electrical Engineering