Abstract
The sharp point of a cone is known to accumulate charges,
thus representing a singularity for the electric field.
However, a real pointed object has a finite radius of
curvature at the apex. Thus, we investigate in this paper
how the 'roundness' affects the behaviour of fields and
charges at the tip of a cone. Two cases are considered: a
double cone being the asymptote of a two-sided
hyperboloid of two sheets and a one-sided cone being the
asymptote of a similar one-sided hyperboloid. Our
analysis employs the prolate spheroidal system of
coordinates and uses Legendre functions of the first kind
of non-integer degree. The behaviour of the surface
charge density is illustrated graphically in terms of the
distance to the apex. Simple approximate formulas for the
charge density valid near the apex are given
Original language | English |
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Article number | 015019 |
Journal | European Journal of Physics |
Volume | 35 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2014 |
MoE publication type | A1 Journal article-refereed |