📚 A-Level Physics: Eddy Currents, Generators and Transformers – Induction in Action | A-Level 物理：涡电流、发电机与变压器的感应应用
Electromagnetic induction is one of the most powerful ideas in A-Level Physics. It explains how a changing magnetic field can create an electric current, and it forms the basis of generators, transformers and many practical devices. This article focuses on three key applications: eddy currents, generators and transformers, and how they demonstrate induction in action.
电磁感应是 A-Level 物理中最重要的概念之一。它解释了变化的磁场如何产生电流，并且是发电机、变压器及许多实用设备的基础。本文将聚焦三个关键应用：涡电流、发电机和变压器，展示感应现象在实际中的运用。
1. Faraday’s Law and Lenz’s Law – The Foundation | 法拉第定律与楞次定律——感应现象的基础
Faraday’s law states that the magnitude of the induced electromotive force (e.m.f.) in a circuit is directly proportional to the rate of change of magnetic flux linkage. The equation is:
法拉第定律指出，回路中感应电动势的大小与磁通匝链数的变化率成正比。其方程为：
E = −N ΔΦ / Δt
where E is the induced e.m.f. in volts, N is the number of turns on the coil, Φ is the magnetic flux in webers, and t is time in seconds. The negative sign comes from Lenz’s law, which states that the direction of the induced current opposes the change that produced it.
其中 E 为感应电动势，单位伏特；N 为线圈匝数；Φ 为磁通量，单位韦伯；t 为时间，单位秒。负号来自楞次定律，它表明感应电流的方向总是阻碍引起它的磁通变化。
Lenz’s law is essentially a statement of energy conservation. If the induced current helped the change, energy would be created from nothing. Instead, the induced current always does work against the motion or change, converting mechanical energy into electrical energy or heat.
楞次定律本质上是能量守恒的体现。如果感应电流帮助磁通变化，能量就会凭空产生。事实上，感应电流总是阻碍运动或变化，将机械能转化为电能或热能。
2. What Are Eddy Currents? | 什么是涡电流？
When a solid metal block is placed in a changing magnetic field, the changing flux induces circulating currents inside the metal. These currents are called eddy currents because they swirl around like eddies in a river.
当实心金属块置于变化的磁场中时，变化的磁通量会在金属内部感应出环形电流。这些电流被称为涡电流，因为它们像河流中的漩涡一样回旋流动。
Eddy currents are loops of current induced within the body of a conductor. Since the metal has low resistance, these currents can be very large. According to Joule heating, the power dissipated is P = I²R, so significant heat can be generated. Eddy currents also produce their own magnetic fields, which interact with the original field to oppose the change according to Lenz’s law.
涡电流是在导体内部感应出的闭合电流环。由于金属电阻很小，这些电流可能非常大。根据焦耳热公式 P = I²R，会产生可观的热量。同时，涡电流也会产生自己的磁场，根据楞次定律与原始磁场相互作用，阻碍磁通变化。
3. Eddy Currents: Energy Losses and How to Reduce Them | 涡电流：能量损失与减少方法
In transformers, electric motors and generators, eddy currents are undesirable because they dissipate energy as heat. This reduces efficiency and can cause overheating. To minimise eddy current losses, the metal core is laminated.
在变压器、电动机和发电机中，涡电流是不受欢迎的，因为它们会以热的形式耗散能量，降低效率并可能导致过热。为减少涡电流损失，铁芯采用叠片结构。
A laminated core is made of thin sheets of iron, each coated with a thin layer of insulating varnish. The insulating layers break the paths of the eddy currents, restricting them to small loops within each sheet. This reduces the magnitude of the eddy currents and therefore the I²R heating loss.
叠片铁芯由薄铁片制成，每片涂有薄层绝缘漆。绝缘层切断了涡电流的路径，将其限制在每片内部的微小环路中，从而减小涡电流的大小，降低 I²R 热损耗。
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Eddy currents are reduced by lamination, not eliminated completely.
叠片只能减小涡电流，不能完全消除。
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Using materials with higher electrical resistivity, such as silicon steel, also reduces eddy currents.
使用电阻率更高的材料，如硅钢，也能减小涡电流。
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In high-frequency applications, ferrite cores are used because their resistivity is much higher than iron.
在高频应用中，使用铁氧体磁芯，因为其电阻率远高于铁。
4. Applications of Eddy Currents: Braking and Heating | 涡电流的应用：制动与加热
Although eddy currents cause energy loss in transformers, they are useful in other applications. One important application is eddy current braking, used in trains and theme park rides. A metal disc or rail moves through a magnetic field, and eddy currents induced in the metal create a drag force that opposes the motion.
尽管涡电流在变压器中造成能量损失，但在其他应用中却非常有用。一个重要的应用是涡电流制动，用于列车和游乐园设施。金属盘或轨道穿过磁场时，金属中感应的涡电流产生阻力，阻碍运动。
The braking force is smooth and contactless, so there is no mechanical wear. The kinetic energy of the moving object is converted into heat in the metal. Eddy current brakes are therefore reliable and require little maintenance.
这种制动力平稳且无接触，因此没有机械磨损。运动物体的动能转化为金属中的热量。涡电流制动器因而可靠且维护需求低。
Another application is induction heating. A metal object is placed in a rapidly alternating magnetic field, and eddy currents heat it from within. This is used in induction cooktops and in industrial processes such as melting metals or sealing containers.
另一个应用是感应加热。将金属物体置于快速交变磁场中，涡电流使其内部发热。这用于电磁炉以及熔炼金属或封装容器的工业过程。
5. The AC Generator: Converting Mechanical Energy to Electrical Energy | 交流发电机：将机械能转化为电能
An alternating current (AC) generator, also called an alternator, converts mechanical energy into electrical energy using electromagnetic induction. The basic structure consists of a coil rotating in a uniform magnetic field, with slip rings and brushes connecting the coil to an external circuit.
交流发电机又称交流发电机，利用电磁感应将机械能转化为电能。基本结构包括在均匀磁场中旋转的线圈，通过滑环和电刷将线圈连接到外部电路。
As the coil rotates, the magnetic flux through the coil changes continuously. The induced e.m.f. varies sinusoidally with time. When the plane of the coil is parallel to the magnetic field, the flux is zero but the rate of change of flux is maximum, so the e.m.f. is maximum. When the plane is perpendicular to the field, the flux is maximum but the rate of change is zero, so the e.m.f. is zero.
当线圈旋转时，穿过线圈的磁通量持续变化。感应电动势随时间呈正弦变化。当线圈平面平行于磁场时，磁通量为零但磁通变化率最大，因此电动势最大；当线圈平面垂直于磁场时，磁通量最大但变化率为零，因此电动势为零。
E = E₀ sin(ωt)
where E₀ is the peak e.m.f. and ω is the angular frequency of rotation. The frequency of the output is determined by the rotational speed of the coil.
其中 E₀ 为峰值电动势，ω 为旋转角频率。输出频率由线圈的转速决定。
6. Generator Characteristics: EMF, Frequency and Output | 发电机的特性：电动势、频率与输出
For a simple generator with a single coil, the peak e.m.f. depends on several factors: the magnetic flux density B, the area A of the coil, the number of turns N, and the angular velocity ω. The peak e.m.f. is given by:
对于单线圈简单发电机，峰值电动势取决于以下因素：磁通密度 B、线圈面积 A、匝数 N 和角速度 ω。峰值电动势为：
E₀ = BANω
This equation shows that increasing any of these factors increases the output voltage. In real power stations, generators use strong electromagnets, many turns, and rotate at high speed to produce high voltages.
该方程表明，增大任一因素都会提高输出电压。在真实发电站中，发电机使用强电磁铁、多匝线圈并以高速旋转，以产生高电压。
The output frequency of a mains generator is fixed at 50 Hz in the UK and many other countries. This is achieved by maintaining a constant rotational speed. A steam turbine or water turbine provides the mechanical input, and the generator converts the rotational kinetic energy into electrical energy.
电网发电机的输出频率在英国及其他许多国家固定为 50 Hz，这通过保持恒定转速来实现。蒸汽轮机或水轮机提供机械输入，发电机将旋转动能转化为电能。
In CIE A-Level examinations, it is important to be able to sketch the graph of e.m.f. against time for an AC generator, and to explain why the e.m.f. is zero when the coil is perpendicular to the magnetic field.
在 CIE A-Level 考试中，重要的是能够绘制交流发电机的电动势-时间图像，并解释为什么当线圈垂直于磁场时电动势为零。
7. Transformers: Principles of Operation | 变压器的工作原理
A transformer is a device that changes the voltage of an alternating current using electromagnetic induction. It consists of a primary coil, a secondary coil and a soft iron core. The primary coil is connected to an alternating voltage source, and the secondary coil is connected to the output circuit.
变压器是一种利用电磁感应改变交流电压的装置。它由初级线圈、次级线圈和软铁芯组成。初级线圈连接到交流电源，次级线圈连接到输出电路。
The alternating current in the primary coil produces a changing magnetic flux in the iron core. Because the core is made of soft iron, it is easily magnetised and demagnetised, and it channels the magnetic flux through the secondary coil. The changing flux in the secondary coil induces an alternating e.m.f. across it.
初级线圈中的交流电流在铁芯中产生变化的磁通。由于铁芯由软铁制成，容易被磁化和退磁，并将磁通引导通过次级线圈。次级线圈中变化的磁通感应出交变电动势。
For an ideal transformer with no energy losses, the power input equals the power output:
对于无能量损失的理想变压器，输入功率等于输出功率：
Vₚ Iₚ = Vₛ Iₛ
where Vₚ and Iₚ are the primary voltage and current, and Vₛ and Iₛ are the secondary voltage and current.
其中 Vₚ 和 Iₚ 是初级电压和电流，Vₛ 和 Iₛ 是次级电压和电流。
8. Transformer Equation and Efficiency | 变压器方程与效率
The relationship between the number of turns and the voltage in a transformer is given by the transformer equation:
变压器中匝数与电压的关系由变压器方程给出：
Vₛ / Vₚ = Nₛ / Nₚ
where Nₚ is the number of turns on the primary coil and Nₛ is the number of turns on the secondary coil. This equation applies to an ideal transformer where all the magnetic flux is linked with both coils.
其中 Nₚ 是初级线圈匝数，Nₛ 是次级线圈匝数。该方程适用于所有磁通都与两个线圈交链的理想变压器。
If Nₛ > Nₚ, the transformer is a step-up transformer, increasing the voltage. If Nₛ < Nₚ, it is a step-down transformer, decreasing the voltage. Step-up transformers are used at power stations to increase voltage for transmission, while step-down transformers reduce voltage for domestic use.
如果 Nₛ > Nₚ，则为升压变压器，电压升高；如果 Nₛ < Nₚ，则为降压变压器，电压降低。发电站使用升压变压器升高电压以便传输，而降压变压器将电压降低以供家庭使用。
The efficiency of a transformer is the ratio of output power to input power:
变压器的效率是输出功率与输入功率之比：
efficiency = (Vₛ Iₛ) / (Vₚ Iₚ) × 100%
Real transformers are not perfectly efficient because of energy losses. In A-Level questions, you may be asked to calculate the efficiency of a transformer given input and output powers, or to explain why high-voltage transmission reduces energy loss.
实际变压器并非完全高效，因为存在能量损失。在 A-Level 题目中，你可能会被要求根据输入和输出功率计算变压器效率，或解释为什么高压输电能减少能量损失。
9. Core Losses and Modern Improvements | 铁芯损耗与现代改进
Transformers have several sources of energy loss. Copper losses occur because the windings have resistance, so I²R heat is generated in the wires. To reduce this, thick copper wire is used for the windings.
变压器存在多种能量损失来源。铜损是由于绕组有电阻，导线中产生 I²R 热量。为减少铜损，绕组使用粗铜线。
Eddy current losses in the iron core are reduced by laminating the core, as described earlier. Hysteresis losses arise because the iron core is repeatedly magnetised in opposite directions, and energy is lost in overcoming the magnetic domain friction. Using soft iron with a narrow hysteresis loop minimises this loss.
铁芯中的涡电流损失通过叠片来减小，如前所述。磁滞损耗源于铁芯反复反向磁化，克服磁畴摩擦消耗能量。使用磁滞回线窄的软铁可以最小化这种损耗。
Flux leakage is another source of inefficiency: some magnetic field lines do not pass through the secondary coil. In modern transformers, the core is designed as a closed loop, such as a rectangular or toroidal shape, to minimise leakage.
漏磁是另一个低效来源：部分磁感线没有穿过次级线圈。在现代变压器中，铁芯设计为闭合回路，如矩形或环形，以尽量减少漏磁。
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Copper loss is reduced by using thick, low-resistance wire.
使用粗而低电阻的导线减小铜损。
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Eddy current loss is reduced by laminated cores.
叠片铁芯减小涡电流损失。
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Hysteresis loss is reduced by using soft magnetic materials.
使用软磁材料减小磁滞损耗。
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Flux leakage is reduced by designing a closed magnetic circuit.
设计闭合磁路减小漏磁。
10. Worked Examples | 例题解析
Example 1: Generator e.m.f. A coil of 200 turns and area 4.0 × 10⁻³ m² rotates at 50 revolutions per second in a magnetic field of 0.20 T. Calculate the peak e.m.f.
例 1：发电机电动势。一个 200 匝、面积为 4.0 × 10⁻³ m² 的线圈在 0.20 T 的磁场中以每秒 50 转旋转。计算峰值电动势。
Solution: The angular velocity is ω = 2πf = 2π × 50 = 314 rad s⁻¹. Using E₀ = BANω:
解：角速度 ω = 2πf = 2π × 50 = 314 rad s⁻¹。使用 E₀ = BANω：
E₀ = 0.20 × 4.0 × 10⁻³ × 200 × 314 = 50 V
Example 2: Transformer voltage. A step-up transformer has 400 turns on the primary and 12 000 turns on the secondary. If the primary voltage is 230 V, calculate the secondary voltage.
例 2：变压器电压。一台升压变压器初级有 400 匝，次级有 12 000 匝。如果初级电压为 230 V，计算次级电压。
Solution: Using Vₛ / Vₚ = Nₛ / Nₚ:
解：使用 Vₛ / Vₚ = Nₛ / Nₚ：
Vₛ = 230 × 12 000 / 400 = 6900 V
Example 3: Eddy current loss. A transformer has an input power of 500 W and an output power of 450 W. Calculate the efficiency and the total power loss.
例 3：涡电流损失。一台变压器输入功率为 500 W，输出功率为 450 W。计算效率与总功率损失。
Solution: efficiency = (450 / 500) × 100% = 90%. The power loss is 500 − 450 = 50 W.
解：效率 = (450 / 500) × 100% = 90%。功率损失为 500 − 450 = 50 W。
11. Common Exam Mistakes and Tips | 常见考试错误与提示
A common mistake is using DC current in transformer calculations. Transformers only work with alternating current because a changing current is required to produce a changing magnetic flux. Steady DC produces no induced e.m.f. in the secondary coil.
常见错误是在变压器计算中使用直流电。变压器只能使用交流电工作，因为需要变化的电流产生变化的磁通。恒定直流电不会在次级线圈中感应出电动势。
Another mistake is confusing Faraday’s law with Lenz’s law. Faraday’s law gives the magnitude of the induced e.m.f., while Lenz’s law gives its direction. Always remember the negative sign in E = −N ΔΦ / Δt.
另一个错误是混淆法拉第定律与楞次定律。法拉第定律给出感应电动势的大小，楞次定律给出其方向。始终记住 E = −N ΔΦ / Δt 中的负号。
When drawing the e.m.f.–time graph for a generator, make sure the curve is sinusoidal and that it crosses zero at the correct points. The maximum e.m.f. occurs when the coil is parallel to the magnetic field, not when it is perpendicular.
绘制发电机电动势-时间图像时，确保曲线为正弦曲线，并在正确的点过零。最大电动势出现在线圈平行于磁场时，而非垂直于磁场时。
For transformer questions, check whether the transformer is step-up or step-down before applying the equation. If Nₛ > Nₚ, the voltage increases and the current decreases proportionally.
在变压器问题中，应用方程前先判断是升压还是降压。如果 Nₛ > Nₚ，电压升高而电流成比例减小。
12. Summary | 总结
Eddy currents, generators and transformers are three key applications of electromagnetic induction. Eddy currents are circulating currents induced in conductors; they cause energy loss in cores but are useful in braking and heating. AC generators convert mechanical energy into sinusoidal electrical energy using a rotating coil in a magnetic field. Transformers use a changing magnetic flux in an iron core to step voltage up or down efficiently.
涡电流、发电机和变压器是电磁感应的三个关键应用。涡电流是导体中感应出的环形电流；它们导致铁芯能量损失，但在制动和加热中很有用。交流发电机通过在磁场中旋转线圈将机械能转化为正弦交流电能。变压器利用铁芯中变化的磁通高效地升高或降低电压。
Understanding these applications requires a solid grasp of Faraday’s law and Lenz’s law. By mastering the equations, graphs and practical design features such as lamination, you will be well prepared for CIE A-Level Physics questions on electromagnetic induction.
理解这些应用需要扎实掌握法拉第定律和楞次定律。通过掌握方程、图像以及叠片等实际设计特征，你将能够从容应对 CIE A-Level 物理中关于电磁感应的题目。
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