📚 Using Induction: Eddy Currents, Generators and Transformers | 感应应用：涡流、发电机与变压器
Electromagnetic induction allows us to convert mechanical energy into electrical energy and vice versa. In this article, we explore three major applications: eddy currents, generators and transformers. Understanding these concepts is crucial for A-Level Physics, as they tie together Faraday’s law, Lenz’s law and energy conservation in real‑world devices.
电磁感应使我们能够将机械能转化为电能，反之亦然。本文探讨三个主要应用：涡流、发电机和变压器。理解这些概念对 A-Level 物理至关重要，因为它们将法拉第定律、楞次定律和能量守恒与实际设备联系起来。
1. Recap of Electromagnetic Induction | 电磁感应复习
emf is given by Faraday’s law: ε = − ΔΦ/Δt, where the negative sign represents Lenz’s law.
当穿过电路的磁通量 Φ 发生变化时，会感应出电动势。感应电动势的大小由法拉第定律给出：ε = − ΔΦ/Δt，其中负号代表楞次定律。
, where B is the magnetic flux density, A is the area of the coil, and θ is the angle between the field lines and the normal to the area. The unit of flux is the weber (Wb).
磁通量定义为 Φ = B A cos θ，其中 B 是磁通密度，A 是线圈面积，θ 是磁感线与面积法线之间的夹角。磁通量的单位是韦伯（Wb）。
Lenz’s law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it. This is a consequence of the conservation of energy.
楞次定律指出，感应电流的方向总是使其阻碍产生该电流的磁通量变化。这是能量守恒的结果。
2. Lenz’s Law and Eddy Currents | 楞次定律与涡流
Eddy currents are circulating currents induced in a bulk piece of conductor when it experiences a changing magnetic field. They flow in closed loops perpendicular to the magnetic field, much like tiny whirlpools.
涡流是在块状导体中当磁场变化时感应出的环流。它们在垂直于磁场方向的闭合回路中流动，就像微小的漩涡。
When a solid metal plate moves into a magnetic field, the flux through the leading edge increases, inducing an eddy current that creates a magnetic field opposing the motion. This results in a braking force.
当一块实心金属板进入磁场时，前缘的磁通量增加，感应出涡流，涡流产生的磁场阻碍运动，从而产生制动阻力。
ationary, the changing flux induces eddy currents that generate heat according to P = I²R.
类似地，如果导体静止而磁场变化，变化的磁通量会感应出涡流，根据焦耳定律 P = I²R 产生热量。
3. Eddy Current Braking and Heating | 涡流制动与加热
Eddy currents are used in electromagnetic braking systems, such as those in some trains and roller coasters. A strong magnet is brought close to a rotating metal disc; the induced eddy currents produce a torque that opposes rotation, smoothly slowing the system without friction contact.
涡流用于电磁制动系统，例如某些火车和过山车。强磁铁靠近旋转的金属盘，感应涡流产生阻碍旋转的力矩，平滑地减慢系统速度，且无摩擦接触。
Induction heating exploits eddy currents to heat metals rapidly. A high‑frequency alternating current passes through a coil, generating a changing magnetic field that induces eddy currents inside the metal object, causing it to heat up. This technique is used in induction cookers and metal hardening.
感应加热利用涡流快速加热金属。高频交变电流通过线圈，产生变化的磁场，在金属物体内部感应出涡流，使其升温。这种技术用于电磁炉和金属淬火。
The heating effect also explains why the cores of transformers and motors are not made from solid iron but are laminated – to minimise eddy current losses.
这种热效应也解释了为何变压器和电机铁芯不使用实心铁而采用叠片结构——以最大限度地减少涡流损耗。
4. Minimising Eddy Currents | 减少涡流
In many devices, eddy currents are undesirable because they waste energy as heat. To reduce them, the cores of transformers and the armatures of motors are made of thin, insulated laminations stacked together.
在许多设备中，涡流是不受欢迎的，因为它们以热的形式浪费能量。为减少涡流，变压器铁芯和电机电枢由薄且绝缘的叠片层叠而成。
The insulation between laminations restricts eddy current paths to small loops, increasing the effective resistance and thus reducing the currents and associated I²R losses. The plane of the laminations is oriented parallel to the magnetic field lines to further restrict the flow.
叠片之间的绝缘将涡流路径限制在小回路内，增大了有效电阻，从而减小电流和相关 I²R 损耗。叠片平面平行于磁感线方向，以进一步限制涡流。
Ferrite cores, used in high‑frequency transformers, have very high resistivity and naturally suppress eddy currents.
用于高频变压器的铁氧体磁芯电阻率非常高，可自然抑制涡流。
5. The AC Generator (Alternator) | 交流发电机
A simple AC generator consists of a rectangular coil rotating in a uniform magnetic field. The coil is connected to an external circuit via slip rings and carbon brushes, which allow the coil to rotate while maintaining electrical contact.
简单的交流发电机由一个在匀强磁场中旋转的矩形线圈构成。线圈通过滑环和碳刷连接到外部电路，滑环允许线圈旋转同时保持电接触。
sinusoidally: Φ = B A cos θ. If the coil rotates at constant angular speed ω, then θ = ωt.
随着线圈旋转，线圈法线与磁场之间的角度 θ 发生变化，导致磁链呈正弦变化：Φ = B A cos θ。若线圈以恒定角速度 ω 旋转，则 θ = ωt。
dΦ/dt. This yields an alternating emf: ε = N B A ω sin(ωt). The peak emf is ε₀ = N B A ω.
感应电动势是 N 匝线圈磁链的负变化率：ε = − N dΦ/dt。由此得到交变电动势：ε = N B A ω sin(ωt)。峰值电动势为 ε₀ = N B A ω。
The output is sinusoidal and reverses direction every half cycle, hence ‘ rrent’. The frequency f of the generated emf is related to the angular speed by ω = 2 π f.
输出是正弦波形，每半个周期方向反转，因此称为“交变电流”。发电电动势的频率 f 与角速度的关系为 ω = 2π f。
6. EMF Equation of a Generator | 发电机的电动势方程
For a coil of N turns, area A rotating at angular speed ω in a uniform magnetic field B, the instantaneous induced emf is:
对于 N 匝、面积为 A 的线圈在匀强磁场 B 中以角速度 ω 旋转，瞬时感应电动势为：
ε = N B A ω sin(ωt) = ε₀ sin(ωt)
coil is parallel to the field lines (θ = 90°), giving the greatest rate of change of flux.
最大电动势 ε₀ 出现在 sin(ωt) = 1 时，即线圈平面与磁感线平行（θ = 90°），此时磁通量变化率最大。
rpendicular to the field (θ = 0° or 180°), where flux is maximum but momentarily constant.
当线圈垂直于磁场（θ = 0° 或 180°）时，电动势为零，此时磁通量最大但瞬间不变。
In a practical power station, the coil is usually stationary and the magnet rotates; the physics remains identical.
在实际发电站中，线圈通常静止而磁铁旋转；物理原理完全相同。
7. Introduction to Transformers | 变压器简介
A transformer is a device that changes the voltage of an alternating current using electromagnetic induction. It consists of two coils, the primary and the secondary, wound on a common laminated iron core.
变压器是利用电磁感应改变交流电压的装置。它由两个线圈（初级线圈和次级线圈）绕在共同的叠片铁芯上构成。
When an alternating voltage is applied to the primary coil, it establishes an alternating magnetic flux in the core. This changing flux links the secondary coil, inducing an emf in it according to Faraday’s law.
当初级线圈加上交流电压时，会在铁芯中建立交变磁通。这变化的磁通交链次级线圈，依据法拉第定律在次级线圈中感应出电动势。
The core provides a path of high magnetic permeability, ensuring that almost all of the flux produced by the primary passes through the secondary.
铁芯提供高磁导率路径，确保初级线圈产生的几乎全部磁通穿过次级线圈。
Transformers only work with alternating current because a changing flux is essential for induction; a steady direct current would produce no induced emf in the secondary once the field is established.
变压器只能使用交流电，因为感应需要变化的磁通；稳定的直流电在磁场建立后不会在次级线圈中感应出电动势。
8. The Ideal Transformer Equation | 理想变压器方程
In an ideal transformer, there is no flux leakage and no energy loss. The ratio of the secondary voltage Vₛ to the primary voltage Vₚ equals the ratio of the number of turns:
在理想变压器中，无磁漏且无能量损失。次级电压 Vₛ 与初级电压 Vₚ 之比等于匝数之比：
Vₛ / Vₚ = Nₛ / Nₚ
This is called the turns ratio equation. A step‑up transformer has Nₛ > Nₚ, making Vₛ > Vₚ. A step‑down transformer has Nₛ < Nₚ, making Vₛ < Vₚ.
这称为匝数比方程。升压变压器 Nₛ > Nₚ，使 Vₛ > Vₚ。降压变压器 Nₛ < Nₚ，使 Vₛ < Vₚ。
ower equals the output power: Pₚ = Pₛ. Since P = I V, we obtain Iₚ Vₚ = Iₛ Vₛ, leading to:
对于理想变压器，输入功率等于输出功率：Pₚ = Pₛ。由 P = I V 可得 Iₚ Vₚ = Iₛ Vₛ，从而：
Iₚ / Iₛ = Nₛ / Nₚ = Vₛ / Vₚ
Thus, in a step‑up transformer, the current in the secondary is smaller than in the primary, and vice versa.
因此，在升压变压器中，次级电流小于初级电流，反之亦然。
9. Transformer Losses and Efficiency | 变压器损耗与效率
Real transformers are not 100% ral mechanisms. The efficiency η is defined as (useful output power) / (input power) × 100%.
实际变压器的效率并非 100%。能量因多种机制而损失。效率 η 定义为（有用输出功率）/（输入功率）× 100%。
Copper losses (I²R losses) occur in the resistance of the windings. They can be reduced by using thick copper wire to lower resistance.
铜耗（I²R 损耗）发生在绕组电阻中。可通过使用粗铜线降低电阻来减少。
Eddy current losses occur in the iron core, as discussed earlier. Laminating the core restricts eddy currents and greatly reduces this loss.
涡流损耗发生在铁芯中，如前所述。铁芯叠片可限制涡流，并极大减少这一损失。
Hysteresis loss arises from the repeated magnetisation and demagnetisation of the core material. Using a ‘soft’ magnetic material with a narrow hysteresis loop minimises this energy loss.
磁滞损耗因铁芯材料反复磁化和去磁而产生。使用磁滞回线狭窄的“软”磁性材料可最大限度地减少这种能量损失。
Flux leakage occurs when some of the magnetic flux produced by the primary does not link the secondary. A well‑designed core with overlapping E‑I laminations reduces leakage.
磁漏是指初级产生的部分磁通没有交链次级。设计良好的 EI 叠加铁芯可减少磁漏。
10. Power Transmission and Step‑up/Step‑down | 电力传输与升压/降压
Electricity is generated at power stations at around 25 kV. To transmit power over long distances with minimal losses, step‑up transformers raise the voltage to several hundred kilovolts (e.g. 400 kV).
发电站发出的电大约为 25 kV。为以最小损耗远距离输电，升压变压器将电压升至数百千伏（如 400 kV）。
in the cables is Ploss = I² R, reducing the current dramatically cuts transmission losses.
对于给定的传输功率 P = I V，电压越高则电流越低。由于电缆中的功率损耗为 Ploss = I² R，降低电流可大幅减少传输损耗。
At the consumer end, step‑down transformers progressively reduce the voltage to safe levels, such as 230 V for homes.
在用户端，降压变压器逐级将电压降低至安全水平，例如家庭用电 230 V。
This system of high‑voltage transmission and local distribution makes the national grid efficient and economical.
这种高压输电与本地配电系统使得国家电网高效且经济。
11. Worked Examples and Calculations | 例题与计算
Example 1: An ideal transformer has 500 primary turns and 50 secondary turns. The primary is connected to a 240 V AC mains. Find the secondary voltage.
例 1：一台理想变压器有 500 匝初级线圈和 50 匝次级线圈。初级接 240 V 交流电源。求次级电压。
Using Vₛ / Vₚ = Nₛ / Nₚ → Vₛ = (Nₛ / Nₚ) Vₚ = (50/500) × 240 V = 24 V. This is a step‑down transformer.
由 Vₛ / Vₚ = Nₛ / Nₚ → Vₛ = (Nₛ / Nₚ) Vₚ = (50/500) × 240 V = 24 V。这是一台降压变压器。
Example 2: If the primary current is 2 A, what is the secondary current (ideal case)?
例 2：若初级电流为 2 A，次级电流是多少（理想情况）？
× 2 A = 20 A. Power input = 240 V × 2 A = 480 W; output = 24 V × 20 A = 480 W, consistent.
Iₚ / Iₛ = Nₛ / Nₚ → Iₛ = (Nₚ / Nₛ) Iₚ = (500/50) × 2 A = 20 A。输入功率 = 240 V × 2 A = 480 W；输出 = 24 V × 20 A = 480 W，一致。
Example 3 (Generator): A coil of 100 turns, area 0.05 m² rotates at 50 rev/s in a magnetic field of 0.1 T. Find the peak emf.
例 3（发电机）：一个 100 匝、面积 0.05 m² 的线圈在 0.1 T 的磁场中以 50 rev/s 旋转。求峰值电动势。
ω = 2πf = 2π × 50 rad/s ≈ 314 rad/s. ε₀ = N B A ω = 100 × 0.1 × 0.05 × 314 = 157 V.
ω = 2πf = 2π × 50 rad/s ≈ 314 rad/s。ε₀ = N B A ω = 100 × 0.1 × 0.05 × 314 = 157 V。
12. Summary and Key Points | 总结与要点
Eddy currents are induced in bulk conductors by changing magnetic fields; they cause braking and heating effects, and are minimised by lamination in cores.
涡流由变化磁场在块状导体中感应产生；它们引起制动和热效应，并通过铁芯叠片来减小。
f ε = N B A ω sin(ωt) by rotating a coil in a magnetic field. Slip rings ensure AC output.
交流发电机通过线圈在磁场中旋转产生正弦电动势 ε = N B A ω sin(ωt)。滑环确保交流输出。
serves power ideally, and losses arise from copper, eddy currents, hysteresis and leakage.
变压器通过匝数比 Vₛ / Vₚ = Nₛ / Nₚ 改变交流电压。理想情况下功率守恒，损耗来源于铜耗、涡流、磁滞和漏磁。
Mastering these applications gives you a deep understanding of Faraday’s and Lenz’s laws in practical, energy‑conscious technology.
掌握这些应用将使你深入理解法拉第定律和楞次定律在注重能源的实际技术中的应用。
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