📚 Electromagnetic Induction and Transformers | 电磁感应与变压器
Electromagnetic induction is one of the most important discoveries in physics, linking electricity and magnetism. It is the principle behind generators and transformers, which are essential for producing and distributing electrical energy. In the Edexcel IGCSE Science course, you need to understand how a changing magnetic field can induce an e.m.f., how generators convert kinetic energy into electrical energy, and how transformers change the size of an alternating voltage. This article covers Faraday's law, Lenz's law, the a.c. generator, the transformer equation, and the efficient transmission of electricity across the national grid.
电磁感应是物理学中最重要的发现之一，它将电与磁联系在一起。它是发电机和变压器背后的原理，对于电能的生产和输送至关重要。在 Edexcel IGCSE 科学课程中，你需要理解变化的磁场如何感应出电动势，发电机如何将动能转化为电能，以及变压器如何改变交流电压的大小。本文涵盖法拉第定律、楞次定律、交流发电机、变压器方程以及国家电网中高效输电的知识。
1. Magnetic Fields and Flux | 磁场与磁通量
To understand electromagnetic induction, we first recall that a magnetic field exists around a permanent magnet or a current-carrying conductor. Magnetic flux, symbol Φ, describes the total magnetic field passing through a given area. It is measured in webers (Wb). When a coil of wire is placed in a magnetic field, the product of the magnetic flux and the number of turns of the coil is called flux linkage. Flux linkage is especially useful because it tells us how much magnetic field is 'linked' with the circuit.
要理解电磁感应，我们首先回顾永久磁铁或载流导体周围存在磁场。磁通量，符号 Φ，描述了通过某一给定面积的总磁场，单位是韦伯 (Wb)。当线圈置于磁场中时，磁通量与线圈匝数的乘积称为磁链。磁链特别有用，因为它告诉我们有多少磁场与电路“交链”。
Φ = B × A (for uniform field perpendicular to area)
磁通量 = 磁通密度 × 面积 (当均匀磁场垂直于面积时)
n the coil. This quantity is the key to predicting the e.m.f. generated when the magnetic environment changes.
如果磁场不垂直，只使用磁场的垂直分量。磁链 = N × Φ，其中 N 是线圈的匝数。当磁环境发生变化时，这个量是预测感应电动势的关键。
2. Faraday's Law of Electromagnetic Induction | 法拉第电磁感应定律
Michael Faraday discovered that whenever there is a change in the magnetic flux linking a circuit, an electromotive force (e.m.f.) is induced. The magnitude of the induced e.m.f. is directly proportional to the rate of change of flux linkage. Mathematically, Faraday's law states:
迈克尔·法拉第发现，只要与电路交链的磁通量发生变化，就会感应出电动势。感应电动势的大小与磁链的变化率成正比。用数学表达，法拉第定律为：
ε = -N (ΔΦ / Δt)
where ε is the induced e.m.f. in volts (V), N is the number of turns, ΔΦ is the change in magnetic flux in webers (Wb), and Δt is the time taken for the change in seconds (s). The negative sign indicates the direction of the induced e.m.f., explained by Lenz's law. In IGCSE, we often use the average e.m.f. over a time interval.
其中 ε 是感应电动势 (V)，N 是线圈匝数，ΔΦ 是磁通量的变化量 (Wb)，Δt 是发生变化所用的时间 (s)。负号表示感应电动势的方向，由楞次定律解释。在 IGCSE 中，我们常常计算一段时间内的平均电动势。
e key is relative motion between the magnet and the coil, causing a changing flux linkage.
如果磁铁快速推入线圈，Δt 很小，则感应电动势很大。如果磁铁静止不动，ΔΦ = 0，则不会感应出电动势。关键在于磁铁与线圈之间的相对运动，使磁链发生变化。
3. Lenz's Law and Conservation of Energy | 楞次定律与能量守恒
Lenz's law gives the direction of the induced e.m.f. and current. It states: 'The direction of the induced e.m.f. is such that it opposes the change causing it.' This is represented by the minus sign in Faraday's law. For example, if a north pole of a magnet moves towards a coil, the coil will induce a current that creates its own north pole facing the approaching magnet, trying to repel it. This opposition ensures that energy is conserved – you must do work to push the magnet against the repulsive force, and that mechanical work is converted into electrical energy.
楞次定律给出了感应电动势和电流的方向。其表述为：“感应电动势的方向总是阻碍引起它的变化。”法拉第定律中的负号即表示这一点。例如，如果磁铁的北极靠近线圈，线圈会感应出一个电流，使其朝向磁铁的一端形成北极，试图排斥磁铁。这种阻碍确保了能量守恒——你必须克服排斥力对磁铁做功，这些机械功转化为电能。
Similarly, if the north pole is pulled away, the coil induces a south pole to attract the magnet, again opposing the change. Understanding Lenz's law helps in predicting the direction of current in generators. In IGCSE, you may be asked to state the law and explain, for example, why the needle of a galvanometer flicks one way then the other when a magnet is moved in and out of a coil.
同样，如果北极被拉离线圈，线圈会感应出南极来吸引磁铁，再次阻碍变化。理解楞次定律有助于预测发电机中电流的方向。在 IGCSE 中，你可能会被要求陈述这一定律，并解释例如当磁铁插入和拔出线圈时检流计指针为何会左右偏转。
4. The A.C. Generator | 交流发电机
An alternator, or a.c. generator, uses electromagnetic induction to convert mechanical energy into alternating current. It consists of a coil of wire rotating in a uniform magnetic field between poles of a magnet. Slip rings and carbon brushes allow the coil to be connected to an external circuit without tangling the wires. As the coil rotates, the flux linkage changes continuously, inducing an alternating e.m.f.
交流发电机利用电磁感应将机械能转化为交流电。它由一个在磁极间均匀磁场中旋转的线圈组成。滑环和碳刷使线圈能够连接到外部电路而不会使导线缠绕。当线圈旋转时，磁链不断变化，感应出交变电动势。
When the plane of the coil is horizontal (parallel to the field lines), it cuts the field lines at the maximum rate, so the induced e.m.f. is maximum. When the coil is vertical (perpendicular to the field lines), it moves momentarily along the field lines, so the rate of cutting is zero and the e.m.f. is zero. The e.m.f. varies sinusoidally, producing an alternating current whose direction changes every half turn. A graph of e.m.f. against time shows a sine wave.
当线圈平面水平（平行于磁感线）时，它切割磁感线的速率最大，所以感应电动势最大。当线圈垂直（垂直于磁感线）时，它瞬间沿着磁感线运动，切割速率为零，电动势为零。电动势呈正弦变化，产生每半圈改变一次方向的交流电。电动势随时间变化的图像显示为正弦波。
A simple d.c. generator can be made by replacing the two slip rings with a split-ring commutator, which reverses the connections every half turn, giving a pulsating direct current.
将两个滑环换成裂环换向器，就可以制成简单的直流发电机，换向器每半圈反转连接，从而输出脉动直流电。
5. Factors Affecting Induced e.m.f. | 影响感应电动势的因素
From Faraday's law, we can identify several ways to increase the induced e.m.f. in a coil or generator:
根据法拉第定律，我们可以得出几种增大线圈或发电机中感应电动势的方法：
• Increasing the number of turns on the coil, N.
• Increasing the speed of relative motion or rotation, which reduces Δt.
• Using a stronger magnet, which increases the magnetic flux density B and thus ΔΦ.
• Inserting a soft iron core inside the coil, which concentrates the magnetic field lines and increases flux linkage.
• 增加线圈匝数 N。
• 加快相对运动或旋转速度，从而减小 Δt。
• 使用更强的磁铁，增加磁通密度 B，从而增大 ΔΦ。
• 在线圈内部插入软铁芯，使磁感线集中，增大磁链。
In an a.c. generator, rotating the coil faster increases both the size and the frequency of the induced e.m.f. A larger coil area also increases the amplitude, as more flux is swept out per turn.
在交流发电机中，加快线圈转速会同时增大感应电动势的幅值和频率。线圈面积越大，每圈扫过的磁通量越多，振幅也越大。
6. Introduction to Transformers | 变压器简介
A transformer is a device that changes the magnitude of an alternating voltage. It works on the principle of mutual induction and can only function with alternating current. A transformer consists of two coils, the primary coil and the secondary coil, wound on a common soft iron core. When an alternating voltage is applied to the primary coil, it produces a changing magnetic field in the core. The core guides this changing flux through the secondary coil, inducing an alternating e.m.f. across it.
变压器是一种改变交流电压大小的装置。它基于互感原理工作，并且只能使用交流电。变压器由两个线圈——初级线圈和次级线圈——绕在同一个软铁芯上构成。当初级线圈施加交流电压时，会在铁芯中产生变化的磁场。铁芯将变化的磁通导入次级线圈，从而在次级线圈两端感应出交流电动势。
If the secondary coil is part of a complete circuit, an alternating current flows. The frequency of the induced voltage in the secondary is the same as the frequency of the primary supply. The core is usually laminated to reduce energy losses from eddy currents.
如果次级线圈构成闭合回路，就会有交流电流流动。次级线圈感应电压的频率与初级电源的频率相同。铁芯通常采用叠片结构以减少涡流造成的能量损失。
7. The Transformer Equation | 变压器方程
For an ideal transformer (100% efficient), the ratio of the voltages across the primary and secondary coils is equal to the ratio of the number of turns on the coils. This relationship is known as the transformer equation:
对于理想变压器（效率 100%），初级线圈和次级线圈两端的电压之比等于线圈的匝数比。这一关系称为变压器方程：
Vₚ / Vₛ = Nₚ / Nₛ
where:
Vₚ = primary voltage (input voltage)
Vₛ = secondary voltage (output voltage)
Nₚ = number of turns on the primary coil
Nₛ = number of turns on the secondary coil
其中：
Vₚ = 初级电压（输入电压）
Vₛ = 次级电压（输出电压）
Nₚ = 初级线圈匝数
Nₛ = 次级线圈匝数
Also, for an ideal transformer, input power equals output power:
同时，对于理想变压器，输入功率等于输出功率：
Pₚ = Pₛ so IₚVₚ = IₛVₛ
This means that if a transformer steps up the voltage, the current in the secondary coil must decrease proportionally. In practice, transformers are not perfectly efficient, but they can reach efficiencies above 99% in large power transmission units.
这意味着如果变压器升高电压，次级线圈中的电流必须按比例减小。实际上，变压器并非完美，但大型输电网中的变压器效率可达 99% 以上。
8. Step-up and Step-down Transformers | 升压与降压变压器
A step-up transformer has more turns on the secondary coil than on the primary (Nₛ > Nₚ). It increases voltage and decreases current. Step-up transformers are used at power stations to raise the voltage to hundreds of kilovolts for efficient long-distance transmission.
升压变压器次级线圈的匝数多于初级线圈 (Nₛ > Nₚ)。它升高电压并降低电流。发电站使用升压变压器将电压升至数十万伏，以便进行高效的远距离输电。
A step-down transformer has fewer turns on the secondary (Nₛ < Nₚ). It decreases voltage and increases current. These are used in substations and in everyday devices such as phone chargers, where the mains voltage must be reduced to a safe, low voltage.
降压变压器次级线圈匝数少于初级 (Nₛ < Nₚ)。它降低电压并增大电流。变电站和日常设备如手机充电器中均使用降压变压器，将市电电压降低到安全的低电压。
Remember, a transformer cannot change the frequency or convert d.c. voltage. Applying a steady d.c. voltage to the primary would produce a constant magnetic field in the core, giving zero induced e.m.f. in the secondary after the initial switch-on.
记住，变压器不能改变频率，也不能转换直流电压。给初级施加恒定的直流电压会在铁芯中产生恒定的磁场，除初始接通瞬间外，次级不会感应出电动势。
9. Electrical Power Transmission | 电力输送
Electricity is generated at power stations at a typical voltage of about 25 kV. To transmit power over hundreds of kilometres with minimal energy loss, step-up transformers increase the voltage to 132 kV, 275 kV, or even 400 kV. The reason for using high voltage is that for a given amount of power, a higher voltage means a lower current. Since the heating losses in the cables are proportional to I²R, reducing the current dramatically cuts the power wasted as heat.
发电站通常以约 25 kV 的电压发电。为了以最小的能量损耗远距离输送电力，升压变压器将电压提升至 132 kV、275 kV 甚至 400 kV。使用高电压的原因是，对于一定的功率，电压越高，电流越小。由于电缆中的热损耗与 I²R 成正比，减小电流能大幅减少以热能形式浪费的功率。
times smaller. Near cities and homes, step-down transformers reduce the voltage to a safe 230 V (in the UK).
考虑输送 100 MW 的功率。在 25 kV 下，电流为 4000 A；在 400 kV 下，电流仅为 250 A。同样输电线上的热损耗将是原来的 (4000/250)² = 1/256。在靠近城市和家庭的地方，降压变压器将电压降至安全的 230 V（英国标准）。
10. Transformer Losses and Efficiency | 变压器损耗与效率
Real transformers are not perfect; they experience several types of energy loss:
实际变压器并非完美，存在几种能量损耗：
• Copper losses: heating due to the resistance of the coils. Can be reduced by using thicker wire.
• Eddy currents: induced circular currents in the iron core that cause heating. Laminating the core with insulating layers greatly reduces them.
• Hysteresis loss: energy required to magnetise and demagnetise the core continuously. Soft iron is used because it magnetises and demagnetises easily.
• Flux leakage: not all magnetic flux produced by the primary coil links with the secondary. A well-designed core shape minimises this.
• 铜损：线圈电阻引起的发热。可通过使用更粗的导线来减少。
• 涡流：铁芯中感应出的环流，引起发热。将铁芯用绝缘层叠片能大大减少涡流。
• 磁滞损耗：铁芯不断被磁化和去磁所需要的能量。使用软铁是因为它容易磁化和去磁。
• 漏磁：初级线圈产生的磁通并非全部交链次级线圈。设计良好的铁芯形状能最大限度地减少漏磁。
Efficiency = (output power / input power) × 100%. In a well-designed transformer, efficiency can exceed 99%.
效率 = (输出功率 / 输入功率) × 100%。设计良好的变压器效率可超过 99%。
11. Using the Transformer Equation – Worked Example | 变压器方程应用 – 例题
A step-down transformer is used to operate a 12 V, 24 W lamp from the 230 V mains supply. The primary coil has 1150 turns. Calculate: (a) the number of turns on the secondary coil, (b) the current in the primary coil, assuming 100% efficiency.
一台降压变压器用于从 230 V 市电向 12 V、24 W 灯泡供电。初级线圈有 1150 匝。计算：(a) 次级线圈的匝数，(b) 初级线圈中的电流，假设效率 100%。
(a) Using Vₚ/Vₛ = Nₚ/Nₛ → 230/12 = 1150/Nₛ → Nₛ = 1150 × 12 / 230 = 60 turns.
Output power = 24 W, so input power = 24 W. Iₚ = P / Vₚ = 24 / 230 ≈ 0.104 A (or 104 mA).
(a) 利用 Vₚ/Vₛ = Nₚ/Nₛ → 230/12 = 1150/Nₛ → Nₛ = 1150 × 12 / 230 = 60 匝。
(b) 输出功率 = 24 W，因此输入功率 = 24 W。Iₚ = P / Vₚ = 24 / 230 ≈ 0.104 A（即 104 mA）。
Note that if the efficiency were less than 100%, the input power would be greater, and the primary current would be slightly higher. This type of calculation is common in IGCSE Edexcel exams.
注意，如果效率低于 100%，输入功率将更大，初级电流也会略高。这类计算在 Edexcel IGCSE 考试中很常见。
12. Summary and Key Points | 总结与要点
induction occurs whenever there is a change in magnetic flux linkage in a circuit. Faraday's law gives the size of the induced e.m.f., and Lenz' Nₛ. High-voltage transmission reduces current and thus I²R losses, making the National Grid highly efficient. Understanding these principles, along with practical factors affecting efficiency, is essential for Edexcel IGCSE Physics and Science papers.
电磁感应发生在回路中的磁链发生变化时。法拉第定律给出感应电动势的大小，楞次定律给出其方向。交流发电机由磁场中旋转的线圈构成，产生正弦交流电动势。变压器利用互感来升高或降低电压，遵从 Vₚ/Vₛ = Nₚ/Nₛ。高压输电减小电流，从而降低了 I²R 损耗，使得国家电网极为高效。理解这些原理以及影响效率的实际因素，对于应对 Edexcel IGCSE 物理和科学考试至关重要。
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