### 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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### Cite this

*European Journal of Physics*,

*35*(1), [015019]. https://doi.org/10.1088/0143-0807/35/1/015019

}

*European Journal of Physics*, vol. 35, no. 1, 015019. https://doi.org/10.1088/0143-0807/35/1/015019

**Fields and charges near the apex of a hyperbolic cone.** / Stén, Johan; Koivisto, Päivi.

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 -