珀尔帖效应

This law states that the electromotive force (EMF, [latex]\mathcal{E}[/latex]) induced in any closed circuit is equal to the negative of the time rate of change of the magnetic flux ([latex]\Phi_B[/latex]) through the circuit. The mathematical expression is [latex]\mathcal{E} = -\frac{d\Phi_B}{dt}[/latex]. This principle is the basis for electric generators, transformers, and inductors, describing the macroscopic effect of induction.

发电机是一种利用电磁感应将机械能转化为电能的装置。其基本设计包括一个在磁场中旋转的线圈（或一个在线圈内旋转的磁铁）。这种连续旋转会改变穿过线圈的磁通量，从而产生交变电动势 (EMF) 和电流，正如法拉第定律所述。

A reformulation of classical mechanics that uses generalized coordinates and their conjugate momenta. It is based on the Hamiltonian function, [latex]H(q, p, t)[/latex], representing the system's total energy. The dynamics are described by Hamilton's equations: [latex]\dot{q}_i = \frac{\partial H}{\partial p_i}[/latex] and [latex]\dot{p}_i = -\frac{\partial H}{\partial q_i}[/latex]. This framework is central to quantum mechanics and statistical mechanics.

丹尼尔电池是对伏打电堆的改进，它由浸在硫酸铜(II)溶液中的铜电极和浸在硫酸锌溶液中的锌电极组成，中间由多孔屏障隔开。这种双流体设计可防止氢气在铜电极上积聚（极化），从而产生更稳定、更可靠的电压源，并能持续更长时间。

光伏效应是指材料在光照下产生电压和电流。它是一种物理和化学现象。太阳能电池就是一个常见的应用，它利用光伏效应将阳光直接转化为电能。光伏效应的原理是光子激发电子进入更高的能量状态。

A primary source of electromotive force is electromagnetic induction, described by Faraday's law. It states that a time-varying magnetic flux [latex]\Phi_B[/latex] through a circuit loop induces an EMF ([latex]\mathcal{E}[/latex]). The magnitude of the EMF is proportional to the rate of change of the flux, given by the equation [latex]\mathcal{E} = - \frac{d\Phi_B}{dt}[/latex]. This principle is the foundation for electric generators, transformers, and inductors.

As a motor's armature rotates, its conductors cut through the magnetic field, inducing a voltage according to Faraday's law of induction. This 'back-EMF' opposes the main voltage driving the motor. Its magnitude is directly proportional to the motor's rotational speed ([latex]\mathcal{E}_{back} \propto \omega[/latex]). This phenomenon is crucial for the self-regulation of motor speed and current draw.

Self-inductance is the property of an electrical circuit whereby a change in the current flowing through it induces an electromotive force (EMF) in the circuit itself. This 'back EMF' opposes the change in current, as dictated by Lenz's law. The relationship is given by the formula [latex]mathcal{E}_L = -L frac{dI}{dt}[/latex], where L is the self-inductance, measured in Henries (H).

楞次定律规定了电磁感应产生的感应电动势 (EMF) 和电流的方向。该定律指出，感应电流的流动方向与产生磁场的方向相反，磁场的方向与产生磁场的磁通量变化方向相反。这一原理是能量守恒的结果，在法拉第定律中用负号表示。

Catalysis is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst. Catalysts are not consumed in the reaction and remain unchanged. They work by providing an alternative reaction pathway with a lower activation energy ([latex]E_a[/latex]), thereby accelerating both the forward and reverse reactions without altering the overall thermodynamics ([latex]\Delta H[/latex]).

燃料电池是一种电化学装置，它能直接将燃料（通常是氢气）和氧化剂（通常是氧气）的化学能转化为电能。与电池不同，燃料电池需要持续的外部燃料和氧化剂供应才能工作。其核心部件包括阳极、阴极和电解质，电解质将阳极和阴极分隔开来，促进离子传输。