Electric generators convert external energy, such as mechanical, thermal, nuclear, chemical, and so forth, into electricity and are the foundation of power station and energy harvesting operations. Inevitably, the external source supplies a force per unit charge (commonly referred to as an impressed electric field) to free or bound charge, which produces ac electricity. In general, the external impressed force acts outside Maxwell’s equations and supplies a nonconservative electric action generating an oscillating electrodynamic degree of freedom. In this work we analyze the electrodynamics of ideal free- and bound-charge electricity generators by introducing a time-dependent permanent polarization, which exists without any applied electric field, necessarily modifying the constitutive relations and essential to oscillate free or bound charge in a lossless way. For both cases, we show that Maxwell’s equations and, in particular, Faraday’s law are modified, along with the required boundary conditions through the addition of an effective impressed magnetic current boundary source and the impressed electric field, related via the left-hand rule. For the free-charge case, we highlight the example of an electromagnetic generator based on Lorentz force, where the impressed force per unit charge that polarizes the conductor comes from mechanical motion of free electrons due to the impressed velocity of the conductor relative to a stationary dc magnetic field. In contrast, the bound-charge generator is simply an idealized permanently polarized bar electret, where the general case of a time-dependent polarized electret is the underlying principle behind piezoelectric nanogenerators. In the open-circuit state, both bound- and free-charge electricity generators are equivalent to idealized Hertzian dipoles, with the open-circuit voltage equal to the induced electromotive force (emf). Analyzing the short-circuit responses, we show that the bound-charge electricity generator has a capacitive source impedance. In contrast, we show that, for the ideal free-charge ac electricity generator, the back emf from the inductance of the loop that defines the short circuit directly cancels the source emf, so the voltage across the inductor is solely determined by the magnetic current boundary source. Thus, we find that the magnetic current boundary source best describes the output voltage of an ac generator, rather than the electric field.

中文翻译：

---

使用外加电源的自由和有约束电的发电机的电动力学

发电机将机械，热能，核能，化学等外部能源转化为电能，并且是发电站和能源收集业务的基础。不可避免地，外部电源会向自由电荷或束缚电荷提供每单位电荷的力（通常称为外加电场），从而产生交流电。通常，外加力作用于麦克斯韦方程之外，并提供非保守的电作用，产生振荡的电动自由度。在这项工作中，我们通过引入随时间变化的永久极化来分析理想的自由电荷和束缚电荷发电机的电动力学，该永久极化不存在任何外加电场，必须修改本构关系，并且对于以无损方式振荡自由电荷或束缚电荷必不可少。对于这两种情况，我们都证明了麦克斯韦方程组，特别是法拉第定律，以及通过添加有效的施加的磁电流边界源和施加的电场（通过左手定律相关）对所需的边界条件进行了修改。对于自由电荷情况，我们重点介绍基于洛伦兹力的电磁发生器的示例，其中使导体极化的单位电荷的施加力来自自由电子的机械运动，这是由于导体相对于静止物体的施加速度所致直流磁场。相比之下，束缚电荷发生器只是理想化的永久极化条形驻极体，时变极化驻极体的一般情况是压电纳米发电机背后的基本原理。在开路状态下，束缚和自由电荷发电机均等效于理想化的赫兹偶极子，其开路电压等于感应电动势（emf）。分析短路响应，我们表明束缚电荷发生器具有容性源阻抗。相比之下，我们表明，对于理想的免费交流发电机来说，定义短路的环路电感的反电动势会直接抵消源电动势，因此电感器两端的电压仅由磁电流决定边界源。因此，我们发现磁流边界源最能描述交流发电机的输出电压，