电磁力与凝聚系统中的麦克斯韦应力张量
Electromagnetic Force and the Maxwell Stress Tensor in Condensed Systems
摘要：
虽然电磁力在微观上是简单的洛伦兹力，但其宏观形式更为复杂，并由麦克斯韦应力张量和开尔文力等表达式给出。它们的推导相当不透明，有时甚至令人困惑，它们的有效性范围几乎是一个保守的秘密。这些情况不必要地降低了宏观电动力学中某些关键量的有用性和可信度。本文对凝聚介质中的麦克斯韦应力张量和电磁力进行了全面而又有教学意义的推导。它从普遍接受的输入开始：守恒定律，热力学和麦克斯韦方程组。简化被认为是各种限制，特别是平衡，分配给每个表达式的有效性范围。一些普遍存在的误解被仔细审查，并在流行的符号隐藏的歧义揭示。一些典型的强极化系统，特别是铁磁流体的现象，然后考虑。除了增强对这些系统的理解外，它还有助于巩固对引入的概念和导出的公式的掌握，并且它演示了麦克斯韦应力张量可以轻松处理，邀请理论家和实验学家都接受这个有用的量。
英文摘要：
While the electromagnetic force is microscopically simply the Lorentz force, its macroscopic form is more complicated, and given by expressions such as the Maxwell stress tensor and the Kelvin force. Their derivation is fairly opaque, at times even confusing, and their range of validity all but a well kept secret. These circumstances unnecessarily reduce the usefulness and trustworthiness of some key quantities in macroscopic electrodynamics. This article presents a thorough yet pedagogical derivation of the Maxwell stress tensor and electromagnetic force in condensed media. It starts from universally accepted inputs: conservation laws, thermodynamics and the Maxwell equations. Simplifications are considered for various limits, especially the equilibrium, with a range of validity assigned to each expression. Some widespread misconceptions are scrutinized, and hidden ambiguities in popular notations revealed. A number of phenomena typical of strongly polarizable systems, especially ferrofluid, are then considered. In addition to enhancing the appreciation of these systems, it helps to solidify the grasp of the introduced concepts and derived formulas, and it demonstrates the ease with which the Maxwell stress tensor can be handled, inviting theorists and experimentalists alike to embrace this useful quantity.
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