三维欧几里得空间中的静电学注记
Notes on Electrostatics in $\mathbb R^3$
AI总结：
本文提出三维静电学的紧凑表述，推导含非对称主动应力场D_iE_j的机械力泛函，其反对称部分为机械力偶密度。
AI中文摘要：
本文提出了一种紧凑的静电学表述。在不使用本构关系（包括以太关系）的情况下，针对带电区域在势函数下的势能，提出了一种表达式，其中电荷分布由电荷势场确定。假设在电荷的虚运动过程中，电场消耗的虚功等于势能时间导数的负值，推导出了机械力泛函的表达式。该力泛函包含非对称主动应力场D_iE_j的作用，其反对称部分为机械力偶密度。
英文摘要：
A compact formulation of electrostatics is presented. Without using constitutive relations, including the aether relations, an expression for the potential energy of a charged region under a potential function is proposed, where the charge distribution is specified by the charge potential field. Assuming that during a virtual motion of the charge, the virtual work expended by the field is equal to minus the time derivative of the potential energy, an expression for the mechanical force functional is derived. The force functional contains the action of an asymmetric active stress field D_{i}E_{j}, the skew-symmetric part of which is the mechanical couple density.
