📚 Electromagnetic Induction: Key Revision Notes for WJEC A-Level Physics | 电磁感应考点精讲
Electromagnetic induction is one of the most fundamental concepts in A-Level Physics and a regular feature in WJEC examinations. It describes the generation of an electromotive force (emf) across a conductor when it experiences a changing magnetic field. Mastery of Faraday's law, Lenz's law, and their applications in generators, transformers and eddy currents is essential for top marks. This article provides a comprehensive breakdown of the topic with bilingual explanations, key formulas and exam tips.
电磁感应是 A-Level 物理中最基础的概念之一，在 WJEC 考试中频繁出现。它描述了当导体处于变化的磁场中时，导体两端产生电动势的现象。掌握法拉第定律、楞次定律及其在发电机、变压器和涡流中的应用是取得高分的必备条件。本文通过双语讲解、关键公式和备考提示，为你全面梳理该考点。
1. Introduction to Electromagnetic Induction | 电磁感应导论
Electromagnetic induction is the production of an electromotive force (emf) in a conductor whenever the magnetic flux linking that conductor changes. Michael Faraday established the effect experimentally in 1831, and it remains the single most important principle behind electricity generation, transformers and induction motors. In WJEC A-Level Physics you must be able to describe the phenomenon, state the two governing laws, and apply them quantitatively in unfamiliar contexts.
电磁感应是指当导体所交链的磁通量发生变化时，导体中产生电动势（emf）的现象。法拉第于 1831 年通过实验确立了这一效应，它至今仍是发电、变压器和感应电动机背后最重要的原理。在 WJEC A-Level 物理中，你必须能够描述这一现象、表述两条支配定律，并在陌生情境中定量应用它们。
There are only three ways to change the flux linkage of a coil, and essentially every exam question is built on one of them: change the magnetic flux density B, change the area A through which the field passes, or change the angle θ between the field and the coil. If none of these three quantities changes, no emf is induced - a stationary magnet inside a stationary coil gives a reading of precisely zero.
改变线圈磁通链的方式只有三种，几乎所有考题都建立在其一之上：改变磁通密度 B、改变磁场穿过的面积 A，或改变磁场与线圈之间的夹角 θ。只要这三个量都不变，就不会产生感应电动势——静止的磁铁放在静止的线圈中，读数恰好为零。
Standard demonstrations include pushing a bar magnet into a solenoid (a brief deflection of the galvanometer), switching a current on or off in a neighbouring coil, and rotating a coil in a uniform magnetic field. Notice the pattern: it is the change of flux, not the presence of flux, that matters.
标准演示实验包括：把条形磁铁推入螺线管（检流计短暂偏转）、通断相邻线圈中的电流、以及在匀强磁场中旋转线圈。请注意其中的规律：起作用的是磁通量的变化，而不是磁通量本身的存在。
2. Magnetic Flux and Flux Linkage | 磁通量与磁通链
e B is the magnetic flux density in tesla (T) and A is the area in square metres (m²). The unit of flux is the weber (Wb), and 1 Wb = 1 T m².
磁通量 Φ 是穿过给定面积的磁场总量的量度。对于垂直于平面的匀强磁场，Φ = BA，其中 B 是磁通密度，单位为特斯拉（T），A 是面积，单位为平方米（m²）。磁通量的单位是韦伯（Wb），且 1 Wb = 1 T m²。
he field lines and the normal to the area. If the field lies in the plane of the coil, θ = 90° and the flux is exactly zero.
当磁场不垂直于平面时，只有垂直于平面的分量才有贡献，因此 Φ = BA cos θ，其中 θ 是磁感线与面积法线之间的夹角。若磁场位于线圈平面内，则 θ = 90°，磁通量恰好为零。
Φ = B A cos θ (Wb = T × m²)
Flux linkage NΦ extends the idea to a coil of N turns: each turn links the same flux, so the total is N times larger. Flux linkage is measured in weber-turns (Wb turns), and it is flux linkage - never flux alone - that Faraday's law uses.
磁通链 NΦ 把这一概念推广到 N 匝线圈：每一匝交链相同的磁通，所以总量扩大为 N 倍。磁通链的单位是韦伯·匝（Wb·匝），而法拉第定律使用的正是磁通链——绝不是单匝的磁通量。
| Quantity 物理量 | Symbol 符号 | Unit 单位 | Equation 公式 |
| Magnetic flux density 磁通密度 | B | tesla (T) | B = Φ / (A cos θ) |
| Magnetic flux 磁通量 | Φ | weber (Wb) | Φ = B A cos θ |
| Flux linkage 磁通链 | NΦ | Wb turns | NΦ = N B A cos θ |
| Induced emf 感应电动势 | ε | volt (V) | ε = −N ΔΦ / Δt |
3. Faraday's Law of Electromagnetic Induction | 法拉第电磁感应定律
Faraday' rage value over a finite time interval, while ε = −d(NΦ)/dt gives the instantaneous value. The minus sign is a reminder of Lenz's law and is discussed in the next section.
法拉第定律指出，感应电动势的大小与磁通链的变化率成正比。用符号表示，ε = −N ΔΦ/Δt 给出有限时间间隔内的平均值，而 ε = −d(NΦ)/dt 给出瞬时值。式中的负号是对楞次定律的提示，将在下一节讨论。
ε = −N ΔΦ / Δt ε = −d(NΦ) / dt
Three practical consequences follow immediately. Doubling the number of turns N doubles the emf; doubling the speed at which the flux changes doubles the emf; and spreading the same change over a longer time gives a smaller emf. This is exactly why the galvanometer deflection is a brief flick - once the magnet stops moving, the flux stops changing and the emf falls to zero even though flux is still present.
由此可立即得出三个实用结论：匝数 N 加倍，电动势加倍；磁通变化的速度加倍，电动势加倍；同样的变化在更长时间内完成，电动势就更小。这正解释了为什么检流计只出现短暂偏转——磁铁一旦停止运动，磁通就不再变化，即使磁通依然存在，电动势也降为零。
Graphically, on a flux linkage against time graph the induced emf at any instant is the negative of the gradient. The emf is therefore zero at the peaks and troughs of the NΦ - t curve, and maximum where the curve is steepest, namely where it crosses zero. The area under an emf against time graph equals the change in flux linkage, −Δ(NΦ).
从图像上看，在磁通链随时间变化的图线上，任一时刻的感应电动势等于该点斜率的负值。因此电动势在 NΦ - t 曲线的波峰和波谷处为零，而在曲线最陡处（即过零点）达到最大。电动势对时间图像下方的面积等于磁通链的变化量 −Δ(NΦ)。
4. Lenz's Law and Conservation of Energy | 楞次定律与能量守恒
Lenz's law states that the direction of the induced current is such that it opposes the change producing it. If the flux through a coil increases, the induced current creates a field that opposes the increase; if the flux decreases, the induced current creates a field that tries to maintain it. This is the physical meaning of the minus sign in Faraday's law.
楞次定律指出，感应电流的方向总是使它所产生的效应阻碍引起感应电流的变化。若穿过线圈的磁通增加，感应电流产生的磁场就阻碍这一增加；若磁通减少，感应电流产生的磁场则力图维持原有磁通。这就是法拉第定律中负号的物理含义。
Lenz's law is a direct consequence of the conservation of energy. If the induced current aided the change instead of opposing it, the emf would grow without limit and energy would be created from nothing. Instead, work must be done against the magnetic forces, and that mechanical work is converted into electrical energy.
楞次定律是能量守恒的直接结果。假如感应电流助长而非阻碍这一变化，电动势将无限增大，能量就会凭空产生。事实是必须克服磁力做功，而这份机械功被转化为电能。
The classic verification is a strong magnet dropped down a vertical copper tube: copper is non-magnetic, yet the magnet falls slowly because induced eddy currents in the tube wall produce forces that oppose the motion. A similar effect is the jumping ring demonstration, in which a large current suddenly switched in a solenoid induces an opposing current in an aluminium ring and throws it upwards.
经典验证实验是把强
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