以相关 Legendre 多项式三重和的形式对静电势进行圆柱多极扩展

IF 1.9 4区工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC

Journal of Electrostatics Pub Date : 2024-05-20 DOI:10.1016/j.elstat.2024.103932

Filip Vučić

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引用次数: 0

摘要

我们提出了静电势在圆柱坐标中的多极扩展，其中包含相关 Legendre 多项式的三重求和。该扩展的多极矩仅取决于电荷分布，对于圆柱对称电荷分布和其他电荷分布，只需在圆柱坐标中进行简单表示，即可轻松地进行分析计算。为了计算均匀带电固体圆柱体的电势，采用了提出的多极扩展。通过比较均匀带电固体圆柱体产生的电势的多极扩展与已知的圆柱体轴电势表达式，验证了推导出的多极扩展的正确性。

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Cylindrical multipole expansion of electrostatic potential in form of triple sum of associated Legendre polynomials

We present multipole expansion of electrostatic potential in cylindrical coordinates which contains triple summation in terms of associated Legendre polynomials. Multipole moments of presented expansion depend only on charge distribution and can be easily calculated analytically for cylindrically symmetric and other charge distributions with simple representation in cylindrical coordinates. Presented multipole expansion is employed in order to calculate potential of uniformly charged solid cylinder. Correctness of derived multipole expansion is verified by comparing multipole expansion of potential produced by uniformly charged solid cylinder with known expression for potential on its axis.

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来源期刊

Journal of Electrostatics 工程技术-工程：电子与电气

CiteScore

4.00

自引率

11.10%

发文量

审稿时长

49 days

期刊介绍： The Journal of Electrostatics is the leading forum for publishing research findings that advance knowledge in the field of electrostatics. We invite submissions in the following areas: Electrostatic charge separation processes. Electrostatic manipulation of particles, droplets, and biological cells. Electrostatically driven or controlled fluid flow. Electrostatics in the gas phase.