📚 Electromagnetic Induction and Transformers | 电磁感应与变压器
Electromagnetic induction is the process by which a changing magnetic field produces an electromotive force (EMF) in a conductor. This principle, discovered by Michael Faraday, forms the foundation of nearly all modern electrical power generation and is essential for understanding how transformers work. In the IGCSE Edexcel Science specification, you are expected to explain the conditions needed for induction, apply Faraday’s law, use Lenz’s law to predict the direction of induced currents, and describe the structure and operation of generators and transformers. Mastering these ideas will help you analyse real‑world systems ranging from bicycle dynamos to the National Grid.
电磁感应是指变化的磁场在导体中产生电动势（EMF）的过程。这一由迈克尔·法拉第发现的基本原理几乎是所有现代发电技术的基石，也是理解变压器工作原理的关键。在 IGCSE 爱德思科学考纲中，你需要解释产生感应的条件，运用法拉第定律，使用楞次定律判断感应电流的方向，并能描述发电机与变压器的结构和工作方式。掌握这些概念有助于你分析从自行车发电机到国家电网的真实系统。
1. What is Electromagnetic Induction? | 什么是电磁感应？
Electromagnetic induction occurs whenever a conductor moves through a magnetic field, or a magnetic field changes around a conductor. The key requirement is a change in the magnetic flux through a circuit. If you plunge a bar magnet into a coil of wire connected to a sensitive galvanometer, the needle deflects, showing that an EMF has been induced. Pulling the magnet out again induces an EMF in the opposite direction. Holding the magnet stationary generates no EMF – there must be relative motion between the magnet and the coil.
当导体在磁场中运动，或者导体周围的磁场发生变化时，就会发生电磁感应。关键条件是通过回路的磁通量必须发生变化。如果把一根条形磁铁快速插入连接着灵敏电流计的线圈中，指针会偏转，表明产生了感应电动势。把磁铁拉出时，则感应出方向相反的电动势。磁铁静止不动就不会产生电动势——磁铁与线圈之间必须有相对运动。
The strength of the induced EMF can be increased by using a stronger magnet, moving the magnet faster, increasing the number of turns on the coil, or winding the coil around an iron core to concentrate the magnetic field. In a closed circuit, the induced EMF drives a current called the induced current.
增大感应电动势的方法包括：使用更强的磁铁、加快磁铁的运动速度、增加线圈的匝数，或者在线圈中加入铁芯以集中磁场。在闭合回路中，感应电动势会驱动电流流过，这个电流就是感应电流。
2. Faraday’s Law of Induction | 法拉第电磁感应定律
Faraday’s law states that the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linkage through the circuit. In simpler terms, the faster the magnetic field changes inside a coil, the larger the EMF produced. This explains why moving a magnet quickly generates a bigger galvanometer deflection than moving it slowly.
法拉第定律指出，感应电动势的大小与通过电路的磁通量变化率成正比。简单来说，线圈内部的磁场变化越快，产生的电动势就越大。这就解释了为什么快速移动磁铁比缓慢移动磁铁会导致更大的电流计偏转。
For a coil with N turns, the induced EMF ε is given by the relationship: ε ∝ N × (ΔΦ / Δt), where ΔΦ/Δt is the rate of change of magnetic flux. While the exam does not require you to perform calculations with this formula, you must be able to describe the proportionality and predict how changing the number of turns or the speed of movement affects the induced EMF.
对于一个有 N 匝的线圈，感应电动势 ε 满足关系式：ε ∝ N × (ΔΦ / Δt)，其中 ΔΦ/Δt 是磁通量的变化率。虽然考试不要求用该公式进行计算，但你必须能够描述比例关系，并预测改变匝数或运动速度会如何影响感应电动势。
3. Lenz’s Law and Direction of Induced Current | 楞次定律与感应电流方向
Lenz’s law gives the direction of the induced current: it always flows in such a direction as to oppose the change that produced it. This is a consequence of the conservation of energy. If the induced current helped the change, a small push would create a runaway effect, generating unlimited energy – which is impossible.
楞次定律给出了感应电流的方向：感应电流总是沿着这样的方向流动，即要阻碍引起它的变化。这是能量守恒的结果。如果感应电流助长了引起它的变化，那么轻轻的推动就会引发正反馈，产生无限的能量——这是不可能的。
For example, when the north pole of a magnet is pushed into a coil, the coil generates a current that creates its own north pole at the end facing the magnet, repelling the incoming magnet and opposing the motion. When the magnet is pulled out, the coil produces a south pole to attract the magnet, again opposing the change. The work done against this opposition is what converts mechanical energy into electrical energy.
例如，当磁铁的北极被推入线圈时，线圈产生的电流会在靠近磁铁的一端形成自身的北极，排斥靠近的磁铁，阻碍这一运动。当磁铁被拉出时，线圈则产生南极以吸引磁铁，同样是在阻碍变化。克服这种阻碍所做功的过程就是把机械能转化为电能的过程。
4. The Simple A.C. Generator | 简单交流发电机
A basic alternating current (A.C.) generator consists of a rectangular coil of wire that rotates between the poles of a permanent magnet. The ends of the coil are connected to slip rings and carbon brushes, allowing the current to be drawn off without tangling. As the coil rotates, its sides cut through the magnetic field lines, and an EMF is induced.
简单的交流发电机由一个矩形线圈和一对永久磁铁组成，线圈在磁极之间旋转。线圈的两端连接着滑环和碳刷，这样可以在不缠绕导线的情况下将电流引出。随着线圈的转动，它的边会切割磁感线，从而感应出电动势。
The induced EMF changes direction every half‑turn because the side of the coil that was moving upwards switches to moving downwards relative to the field. This produces an alternating current whose voltage follows a sinusoidal pattern. When the coil is perpendicular to the field (vertical in many diagrams), the rate of cutting field lines is momentarily zero, so the EMF is zero at these positions. When the coil is parallel to the field, the rate of cutting is maximum, giving the peak EMF.
每转过半圈，感应电动势的方向就会改变，因为原本向上运动的线圈边变成了向下运动（相对于磁场）。这就产生了电压呈正弦规律变化的交流电。当线圈平面与磁场垂直时（在许多示意图中为竖直位置），切割磁感线的速率瞬间为零，电动势在这些位置也为零。当线圈平面与磁场平行时，切割速率最大，电动势达到峰值。
In contrast, a D.C. generator uses a split‑ring commutator instead of slip rings to reverse the connections every half‑turn, ensuring the current always flows in one direction through the external circuit. This produces a rectified fluctuating direct current.
相比之下，直流发电机使用换向器（裂环整流子）代替滑环，每半圈颠倒一次连接，使得外电路中的电流始终沿一个方向流动，产生经过整流的脉动直流电。
5. Generating Electricity – Induced EMF in Power Stations | 发电——发电站中的感应电动势
In large‑scale power stations, the basic principle remains the same: a turbine spins a large magnet (the rotor) inside a set of stationary coils (the stator), or vice versa. The energy to turn the turbine comes from burning fossil fuels, nuclear fission, falling water, wind, or tides. As the magnetic field sweeps across the coils, an alternating EMF is induced, which is then stepped up using transformers for efficient transmission.
在大型发电站中，基本原理仍然相同：涡轮机带动一块巨大的磁铁（转子）在一组固定线圈（定子）内部旋转，或者反过来让线圈在磁场中旋转。驱动涡轮机的能量来自化石燃料燃烧、核裂变、水的落差、风能或潮汐能。当磁场扫过线圈时，便会感应出交变电动势，然后通过变压器升压以实现高效传输。
An important detail is that increasing the number of poles in the generator and the speed of rotation both increase the frequency of the generated A.C. In the UK, the grid frequency is maintained at 50 Hz, meaning the electromagnet or coil must rotate 50 times per second (or a multiple determined by the number of poles).
一个重要的细节是，增加发电机的磁极数目和提高转速都会增大所产生交流电的频率。在英国，电网频率保持在 50 Hz，这意味着电磁铁或线圈需要每秒旋转 50 次（或由极数决定的相应倍数）。
6. Transformers – Structure and Principle | 变压器——结构和工作原理
A transformer is a device that changes the voltage of an alternating supply. It consists of two insulated coils, the primary and secondary coils, wound around a common soft‑iron core. The core is laminated – made of thin sheets of iron separated by insulating layers – to reduce eddy currents that would waste energy as heat.
变压器是一种用来改变交流电源电压的装置。它由两个绝缘线圈——初级线圈和次级线圈——绕在一个公共的软铁芯上构成。铁芯是叠片状的，由许多薄铁片叠加而成，片间有绝缘层，目的是减少涡流，避免能量以热的形式浪费掉。
When an alternating current flows in the primary coil, it produces a changing magnetic field in the core. The core magnetises and demagnetises in step with the alternating current, channelling the changing magnetic flux through the secondary coil. This changing flux induces an alternating EMF across the secondary coil – exactly the same principle of electromagnetic induction. If the secondary circuit is complete, an alternating current flows.
当初级线圈中流过交流电时，会在铁芯中产生变化的磁场。铁芯随着交流电的节奏反复磁化和退磁，从而将变化的磁通量传递到次级线圈。这个变化的磁通在次级线圈中感应出交变电动势——这正是相同的电磁感应原理。如果次级回路闭合，就会有交流电流过。
7. Step‑up and Step‑down Transformers | 升压变压器和降压变压器
If the secondary coil has more turns than the primary coil, the transformer is called a step‑up transformer. The output voltage is greater than the input voltage, but the current is correspondingly smaller, assuming 100% efficiency. Step‑up transformers are used at power stations to raise the voltage for long‑distance transmission, reducing current and thereby minimising I²R heating losses in the cables.
如果次级线圈的匝数多于初级线圈，这类变压器叫做升压变压器。输出电压高于输入电压，但电流会相应变小（假设效率为 100%）。升压变压器用于发电站将电压升高以便远距离输送，因为电流减小可以降低电缆中的 I²R 发热损耗。
If the secondary coil has fewer turns than the primary coil, it is a step‑down transformer. The output voltage is lower, and the current is larger. Step‑down transformers are used at substations and in everyday appliances, such as phone chargers, to safely reduce the mains voltage to the required level.
如果次级线圈匝数比初级线圈少，它就是降压变压器。输出电压较低，而电流较大。降压变压器用于变电所和日常电器（如手机充电器）中，以便将市电电压安全降低到所需的水平。
8. The Transformer Equation | 变压器方程
For an ideal transformer (one with no energy losses), the ratio of the primary voltage Vₚ to the secondary voltage Vₛ equals the ratio of the number of turns on the primary coil Nₚ to the number of turns on the secondary coil Nₛ. This is expressed by the transformer equation:
对于理想变压器（没有能量损失），初级电压 Vₚ 与次级电压 Vₛ 之比等于初级线圈匝数 Nₚ 与次级线圈匝数 Nₛ 之比，由变压器方程表示：
Vₚ / Vₛ = Nₚ / Nₛ
Because the power input is roughly equal to the power output in an ideal transformer, we can also relate the currents: Vₚ × Iₚ = Vₛ × Iₛ, which leads to Iₚ / Iₛ = Nₛ / Nₚ. These relationships are crucial for solving numerical problems. Remember that this applies only to A.C. – a transformer cannot work with a steady direct current because there would be no changing magnetic field.
由于理想变压器的输入功率约等于输出功率，我们还可以关联电流：Vₚ × Iₚ = Vₛ × Iₛ，由此得出Iₚ / Iₛ = Nₛ / Nₚ。这些关系对于解答计算题至关重要。切记这些只适用于交流电——变压器无法在稳定直流电下工作，因为那样就没有变化的磁场了。
9. Power Transmission and Energy Losses | 电力传输与能量损耗
Electricity is transmitted over long distances at very high voltages, typically 132 kV or higher in the National Grid. The main reason is to reduce the current for a given power, because the heating loss in the cables is proportional to the square of the current: P = I²R. By using step‑up transformers at the generation site, the current is made very small, so the power wasted as heat in the transmission lines drops dramatically.
电力远距离传输时采用非常高的电压，英国国家电网通常为 132 kV 或更高。主要原因是对同样的输送功率，电压越高电流越小，而电缆的发热损耗与电流的平方成正比：P = I²R。在发电端使用升压变压器使电流变得非常小，因此输电线路中以热能形式浪费的功率就大幅减少。
At the consumer end, step‑down transformers lower the voltage to safer values, such as 230 V for homes. This two‑stage process of stepping up and stepping down is far more efficient than transmitting electricity at the voltage at which it is generated. Laminated cores, low‑resistance copper windings, and efficient cooling systems all help minimise the energy wasted inside the transformers themselves.
在用户端，降压变压器将电压降低到更安全的数值，例如家庭用电的 230 V。这种先升后降的两级过程远比以发电时的电压直接传输更高效。叠片铁芯、低电阻铜绕组和高效的冷却系统都有助于减少变压器内部的能量浪费。
10. Efficiency and Practical Considerations | 效率与实际问题
Real transformers are never 100% efficient. Energy is lost through four main mechanisms: resistance heating in the coils (copper losses), eddy currents circulating in the core, hysteresis losses as the core constantly reverses its magnetism, and slight leakage of magnetic flux that does not link both coils. Engineers reduce copper losses by using thicker wire, minimise eddy currents with laminated cores, select magnetically soft materials for the core to lower hysteresis, and design the core shape to channel almost all the flux through both coils.
实际的变压器永远达不到 100% 的效率。能量主要通过四种机制损失：线圈电阻发热（铜损）、铁芯中环流的涡流、铁芯反复磁化带来的磁滞损耗，以及少量未同时环绕两个线圈的漏磁通。工程师通过使用较粗的导线来减少铜损，通过叠片铁芯减小涡流，选择软磁材料降低磁滞，并设计合适的铁芯形状将几乎所有磁通都导入两个线圈。
The efficiency can be calculated as efficiency = (useful power output / total power input) × 100%. A well‑designed large transformer can exceed 99% efficiency, but small plug‑in transformers for electronics often operate at 80‑90% because they are built to a tighter cost budget. Understanding these practical limits helps explain why transformers become warm during operation.
效率可用下式计算：效率 = (有用功率输出 / 总功率输入) × 100%。一个设计精良的大型变压器效率可超过 99%，而小型电子设备的插头式变压器效率则常在 80–90%，因为它们受成本限制较多。了解这些实际限制有助于解释为什么变压器工作时会发热。
11. Key Experimental Demonstrations | 关键实验演示
You should be able to describe a simple experiment to demonstrate electromagnetic induction: connect a coil to a centre‑zero galvanometer, move a bar magnet into and out of the coil, and record the direction and size of the deflection. Repeating the experiment with a faster motion, a stronger magnet, or a coil with more turns shows how each factor affects the induced EMF. Using an iron core inside the coil dramatically increases the galvanometer deflection because iron channels the magnetic field more effectively than air.
你应该能够描述一个展示电磁感应的简单实验：将线圈与中央零位电流计连接，将条形磁铁移入和移出线圈，记录偏转的方向和大小。用更快的速度、更强的磁铁或更多匝数的线圈重复实验，可以显示每种因素如何影响感应电动势。在线圈内部加入铁芯会极大地增加电流计偏转，因为铁比空气更能有效引导磁场。
To investigate transformers, a typical IGCSE practical uses a C‑ xperimental error. The effect of missing the core or using an open core (large air gap) shows how crucial the core is for efficient coupling.
为了研究变压器，典型的 IGCSE 实验会使用一个 C 形铁芯或一对带有可拆卸铁芯的线圈。初级线圈连接交流电源，测量不同匝数下的次级电压。学生验证 Vₚ/Vₛ ≈ Nₚ/Nₛ 在实验误差范围内成立。撤去铁芯或使用留有大气隙的开路铁芯，则说明铁芯对高效耦合至关重要。
12. Linking to the Wider World – National Grid | 与世界连接——国家电网
The National Grid is an excellent real‑world case study. High‑voltage transmission reduces current and therefore thermal losses: if the voltage is stepped up 100 times, the current drops to 1/100 of its original value, and the line loss (I²R) falls by a factor of 10 000. This is why pylons carry cables at 275 kV or 400 kV. Near towns and cities, step‑down transformers reduce the voltage in several stages until it reaches the safe 230 V supply entering our homes. Such an efficient network relies on electromagnetic induction at many points.
国家电网是一个极佳的实际案例。高压输电可以减小电流，从而降低热损耗：如果电压升高至原来的 100 倍，电流就降为原来的 1/100，而线路损耗 (I²R) 则降为原来的万分之一。这就是为什么高压铁塔以 275 kV 或 400 kV 输电。在城镇附近，降压变压器会逐级将电压降低，直至成为进入家庭的 230 V 安全电压。这样高效的网络在多个环节都依赖于电磁感应原理。
Understanding transformers also helps you make sense of electrical safety: double‑insulated transformers isolate the primary from the secondary, protecting the user. Many travel adaptors and power tools use small step‑down transformers for this reason. Recognising these applications reinforces the importance of Faraday’s and Lenz’s laws far beyond the classroom.
理解变压器还能帮助你理解电气安全：双绝缘变压器将初级与次级隔离开，保护使用者。许多旅行转换器和电动工具正是为此使用小型降压变压器。认识这些实际应用会让法拉第定律和楞次定律的意义远远超出课堂。
Published by TutorHao | IGCSE Science Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图