Yakovlev Andrey B., Federyaeva Valeriya S.
Department of Mathematics and Mechanics, Saint Petersburg State University, Saint Petersburg, Russian Federation
An analytical solution is presented for the electric field response generated by a nonconducting ellipsoid (prolate spheroid) in a homogeneous conducting fluid subject to an external primary electric field, including surface charge distribution. Such a solution might be useful for different purposes, including cell modeling subject to an external quasistatic electromagnetic stimulus. The solution utilizes the well-known analogy between the electrostatics of dielectrics and DC conduction. The solution obtained includes an expression for the volumetric fields and an expression for the induced surface charge density at the membrane.
给出了一个解析解，用于求解在均匀导电流体中，受外部主电场作用的非导电椭球体（长椭球体）产生的电场响应，包括表面电荷分布。这样的解可能在不同目的下有用，包括受外部准静态电磁刺激的细胞建模。该解利用了电介质静电学与直流传导之间的著名类比。得到的解包括体积场的表达式和膜上感应表面电荷密度的表达式。
