Faraday’s Law for GCSE Edexcel Physics | 法拉第定律考点精讲

📚 Faraday’s Law for GCSE Edexcel Physics | 法拉第定律考点精讲

Electromagnetic induction is one of the most fundamental principles in physics, explaining how electricity can be generated from magnetism without any physical contact. In GCSE Edexcel Physics, you need to understand Faraday’s law qualitatively – how a changing magnetic field produces an induced potential difference and current, what factors affect the size of this induced e.m.f., and how these ideas are applied in everyday devices such as generators, transformers, microphones and loudspeakers.

电磁感应是物理学中最基本的原理之一，它解释了如何在没有物理接触的情况下通过磁产生电。在 GCSE Edexcel 物理中，你需要定性地理解法拉第定律——变化的磁场如何产生感应电动势和感应电流，哪些因素会影响感应电动势的大小，以及这些原理如何被应用于发电机、变压器、麦克风和扬声器等日常设备中。

1. What is Electromagnetic Induction? | 什么是电磁感应

Electromagnetic induction occurs when a conductor (such as a wire or coil) experiences a changing magnetic field. This changing field causes a potential difference to be induced across the ends of the conductor. If the conductor is part of a complete circuit, an induced current will flow.

当导体（如导线或线圈）处于变化的磁场中时，就会发生电磁感应。这个变化的磁场会使导体两端感应出电势差。如果导体是闭合回路的一部分，就会有感应电流流动。

The key condition is that the magnetic field must be changing – either by moving the magnet relative to the conductor, moving the conductor relative to the magnet, or changing the magnetic field strength itself (e.g. varying the current in a nearby coil).

关键条件是磁场必须发生变化——可以通过磁体与导体之间的相对运动，或者让导体在磁场中运动，或者改变磁场本身的强度（例如改变附近线圈中的电流）。

2. Faraday’s Law of Electromagnetic Induction | 法拉第电磁感应定律

Faraday’s law states that the magnitude of the induced e.m.f. (electromotive force) is directly proportional to the rate of change of magnetic flux linkage. In simple terms, the faster the magnetic field changes, the larger the induced potential difference.

法拉第定律指出，感应电动势的大小与磁链变化率成正比。简单来说，磁场变化得越快，感应出的电势差就越大。

For a coil of wire, the induced e.m.f. can be expressed as:

ε = -N (ΔΦ / Δt)

对于线圈，感应电动势可表示为：

ε = -N (ΔΦ / Δt)

Here, ε is the induced e.m.f. (volts), N is the number of turns in the coil, and ΔΦ/Δt is the rate of change of magnetic flux (measured in webers per second, Wb/s). The minus sign represents Lenz’s law, which gives the direction of the induced e.m.f.

其中 ε 是感应电动势（伏特），N 是线圈匝数，ΔΦ/Δt 是磁通量变化率（单位韦伯每秒）。负号代表楞次定律，用于确定感应电动势的方向。

At GCSE, you are not expected to use this formula for calculations, but you must understand the proportionality: larger N and faster change result in a larger induced e.m.f.

在 GCSE 阶段，你不需要用这个公式进行计算，但必须理解比例关系：线圈匝数越多、变化越快，感应电动势就越大。

3. Magnetic Flux and Flux Linkage | 磁通量与磁链

Magnetic flux (Φ) is a measure of the total magnetic field passing through a given area. It depends on the magnetic field strength (B), the area (A), and the angle between the field and the area. The unit of magnetic flux is the weber (Wb).

磁通量（Φ）是衡量通过给定面积的磁场总量的物理量。它取决于磁感应强度 (B)、面积 (A) 以及磁场与面积之间的夹角。磁通量的单位是韦伯（Wb）。

Magnetic flux linkage is the product of the magnetic flux and the number of turns in a coil: NΦ. This quantity is especially useful for coils. When we change the flux linkage through a coil, an e.m.f. is induced.

磁链是磁通量与线圈匝数的乘积：NΦ。这个量对线圈尤其有用。当通过线圈的磁链发生变化时，就会感应出电动势。

4. Factors Affecting Induced EMF | 影响感应电动势的因素

Several factors determine the size of the induced e.m.f. in a practical experiment, such as moving a magnet into a coil:

在实际实验（如将磁铁插入线圈）中，有几个因素决定感应电动势的大小：

• Speed of movement: The faster the magnet moves relative to the coil, the greater the rate of change of flux, and the larger the induced e.m.f.

  运动速度：磁铁相对于线圈运动得越快，磁通量变化率越大，感应电动势也越大。

• Number of turns (N): More turns on the coil increase the flux linkage, so for the same change in flux, a higher e.m.f. is induced.

  线圈匝数（N）：线圈匝数越多，磁链越大，因此在相同磁通量变化下，感应出的电动势更高。

• Magnetic field strength: A stronger magnet produces a larger magnetic flux, so moving it in and out of the coil gives a bigger change and a bigger e.m.f.

  磁场强度：磁铁越强，产生的磁通量越大，因此将其移入移出线圈时变化更大，感应电动势也更大。

• Area of the coil and orientation: Larger coil area or aligning the coil to cut the field lines at 90 degrees maximises the flux change.

  线圈面积与方向：线圈面积越大，或让线圈以 90 度切割磁感线，可使磁通量变化最大化。

5. Lenz’s Law and Direction of Induced Current | 楞次定律与感应电流方向

Lenz’s law states that the direction of the induced current is always such that it opposes the change in magnetic flux that produced it. This is the 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其阻碍引起感应电流的磁通量变化。这就是法拉第定律中负号的含义。

For example, if you push the north pole of a magnet into a coil, the induced current will create its own north pole at the end of the coil facing the incoming magnet, repelling it. If you pull the magnet out, the induced pole becomes south to attract the magnet back, again opposing the change.

例如，将磁铁的北极推入线圈时，感应电流会在线圈面对磁铁的一端产生一个北极，从而排斥磁铁。如果将磁铁拉出，感应出的磁极变成南极，试图将磁铁拉回来，同样阻碍变化。

This law is a consequence of the conservation of energy: the induced current produces a magnetic force that does negative work on the moving magnet, so mechanical energy is transferred to electrical energy.

这一定律是能量守恒的结果：感应电流产生的磁力对运动的磁铁做负功，从而将机械能转化为电能。

6. Demonstrating Electromagnetic Induction | 演示电磁感应

A classic experiment uses a bar magnet and a coil connected to a sensitive ammeter or galvanometer. No current flows when the magnet is stationary inside the coil. A momentary deflection occurs only when the magnet is moving in or out. The faster the movement, the greater the deflection.

一个经典实验使用条形磁铁和连接灵敏电流计或检流计的线圈。当磁铁在线圈内静止时，没有电流。只有当磁铁移入或移出时，指针才会瞬间偏转。运动越快，偏转越大。

Another simple demonstration uses a straight wire moved between the poles of a horseshoe magnet. A small e.m.f. is induced across the wire, driving a current if the circuit is completed. Reversing the direction of motion or the magnetic field reverses the induced current direction.

另一个简单演示是将直导线在马蹄形磁铁的极间运动。导线两端会产生微小电动势，若电路闭合则产生电流。改变运动方向或磁场方向，感应电流方向也会反转。

7. The Generator Effect and Alternators | 发电机效应与交流发电机

The generator effect is the production of an e.m.f. and current in a conductor moving in a magnetic field. In an alternator, a coil rotates in a fixed magnetic field. As the coil turns, the angle between the coil and the magnetic field changes continuously, causing the flux linkage to change sinusoidally. This produces an alternating current (a.c.).

发电机效应是指导体在磁场中运动时产生电动势和电流。在交流发电机中，线圈在固定磁场中旋转。随着线圈转动，线圈平面与磁场的夹角不断变化，磁链呈正弦变化，从而产生交流电。

Key points for an alternator:

• Slip rings and brushes connect the rotating coil to the external circuit without tangling wires.

  滑环和电刷将旋转线圈与外部电路连接，而不会使导线缠绕。

• The induced e.m.f. is largest when the coil is parallel to the magnetic field (cutting flux at the fastest rate) and zero when the coil is perpendicular (no flux change).

  当线圈平面与磁场平行时（此时切割磁感线速率最快）感应电动势最大；线圈平面与磁场垂直时（无磁通量变化）感应电动势为零。

• Frequency of a.c. depends on rotation speed. Faster rotation gives more cycles per second and also a larger peak e.m.f.

  交流电的频率取决于旋转速度。转速越快，每秒产生的周期数越多，峰值电动势也越大。

8. Transformers and Faraday’s Law | 变压器与法拉第定律

A transformer works on the principle of electromagnetic induction. An alternating current in the primary coil sets up a changing magnetic field in the iron core, which links to the secondary coil. The changing flux induces an alternating e.m.f. in the secondary coil.

变压器基于电磁感应原理工作。初级线圈中的交流电在铁芯中产生变化的磁场，该磁场链接到次级线圈。变化的磁通量在次级线圈中感应出交变电动势。

For an ideal transformer, the ratio of the voltages is equal to the ratio of the number of turns:

Vₚ / Vₛ = Nₚ / Nₛ

对于理想变压器，电压比等于匝数比：

Vₚ / Vₛ = Nₚ / Nₛ

The core is made of soft iron to channel the magnetic field and reduce energy losses. Transformers can step up or step down voltage, but they only work with alternating current because a constant d.c. would produce no changing flux after the initial switch-on.

铁芯由软铁制成，用于引导磁场并减少能量损耗。变压器可以升压或降压，但只能用于交流电，因为恒定的直流电在初始接通后就不再产生变化的磁通量。

9. Applications: Microphones and Loudspeakers | 应用：麦克风与扬声器

A moving-coil microphone uses induction: sound waves cause a diaphragm attached to a coil to vibrate near a permanent magnet. The coil moves in the magnetic field, inducing a varying e.m.f. that matches the sound pattern. This is a direct application of Faraday’s law.

动圈式麦克风利用了电磁感应：声波使附有线圈的振膜在永磁体附近振动。线圈在磁场中运动，感应出与声音模式相应的变化电动势。这是法拉第定律的直接应用。

A loudspeaker works in reverse: a varying electrical signal passes through a coil in a magnetic field, producing a force that moves the coil and attached cone back and forth, generating sound waves.

扬声器则相反：变化的电信号通过磁场中的线圈时产生力，使线圈和附着的锥盆来回运动，从而产生声波。

In both devices, the interaction between a coil, magnet and motion/current exemplifies the motor and generator effects.

在这两种设备中，线圈、磁体与运动/电流之间的相互作用体现了电动机效应和发电机效应。

10. Exam Tips and Common Mistakes | 考试技巧与常见错误

• Always specify “rate of change”: Many students simply say “changing magnetic field produces e.m.f.” without mentioning that the induced e.m.f. depends on how fast the field changes. Use “rate of cutting flux” or “rate of change of flux linkage”.

  一定要说明“变化率”：许多学生只说“变化的磁场产生电动势”，而没有提到感应电动势的大小取决于磁场变化的快慢。使用“切割磁通量的速率”或“磁链变化率”。

• Generator vs motor: Know the generator effect (induction) and motor effect (force on a current-carrying conductor) are distinct. Do not confuse them.

  发电机效应与电动机效应：要清楚发电机效应（感应）和电动机效应（通电导体受力）是不同的，切勿混淆。

• Magnet stationary inside coil: No induced current, because no flux change.

  磁铁在线圈内静止：没有感应电流，因为磁通量没有变化。

• Lenz’s law direction: Practice drawing the coil poles and current direction using the right-hand grip rule. The induced pole always repels or attracts to oppose the motion.

  楞次定律方向：使用右手螺旋定则练习画出线圈磁极和电流方向。感应极总是排斥或吸引以阻碍运动。

• Transformer core: Explain why it is laminated (to reduce eddy currents which cause heating losses). Soft iron is easily magnetised and demagnetised.

  变压器铁芯：解释为何使用叠片铁芯（减少涡流引起的发热损耗）。软铁易于磁化和退磁。

• Equation awareness: You don’t need to memorise complex equations, but understand proportionality: e.m.f. ∝ number of turns × speed of movement × magnet strength.

  公式意识：无需记忆复杂公式，但要理解比例关系：感应电动势 ∝ 匝数 × 运动速度 × 磁体强度。

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Published by TutorHao | Physics Revision Series | aleveler.com

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