Electrostatic potential in cylindrical dielectric media using the image charge method
Electrostatic potential in cylindrical dielectric media using the image charge method
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DOI：
10.1080/00268970600926647
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发表时间：
2006-10-10
影响因子：
1.7
通讯作者：
Cui, S. T.
中科院分区：
文献类型：
--
作者：
Cui, S. T.
本文导出了点电荷在相对介电常数与周围介质不同的圆柱孔中产生的电势的简单解析表达式。孔隙和周围介质之间的界面可以含有电荷或电中性。当周围的电介质与孔或电导体相同时，该表达式简化为已知的解。我们讨论了级数展开的收敛性，并数值计算了圆柱孔内的静电势。计算的电势显示了介质的介电常数差的影响。结果表明，该表达式可用于圆柱形荷电系统的数值动力学模拟。对于源电荷位于圆柱外介质中的情况，我们也给出了一个表达式。
We derive a simple analytical expression for the electric potential produced by a point charge in a cylindrical pore with relative permittivity different from that of the surrounding medium. The interface between the pore and the surrounding media may contain electric charge or be electrically neutral. The expression reduces to the known solutions when the surrounding dielectric medium is identical to the pore or an electric conductor. We discuss the convergence of the series expansion and numerically evaluate the electrostatic potential inside the cylindrical pore. The calculated potential shows the effect of the dielectric permittivity difference of the media. The results demonstrate that the expression can be implemented in a numerical dynamic simulation of charged systems in cylindrical geometry. We also give an expression for the case when the source charge is in the medium outside the cylinder.