Abstract
| Original language | English |
|---|---|
| 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 |
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Fields and charges near the apex of a hyperbolic cone. / Stén, Johan; Koivisto, Päivi.
In: European Journal of Physics, Vol. 35, No. 1, 015019, 2014.Research output: Contribution to journal › Article › Scientific › peer-review
TY - JOUR
T1 - Fields and charges near the apex of a hyperbolic cone
AU - Stén, Johan
AU - Koivisto, Päivi
PY - 2014
Y1 - 2014
N2 - 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
AB - 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
U2 - 10.1088/0143-0807/35/1/015019
DO - 10.1088/0143-0807/35/1/015019
M3 - Article
VL - 35
JO - European Journal of Physics
JF - European Journal of Physics
SN - 0143-0807
IS - 1
M1 - 015019
ER -