Electric Motors & EM Induction | 电动机与电磁感应

📚 Electric Motors & EM Induction | 电动机与电磁感应

Electric motors and electromagnetic induction are two sides of the same coin: motors convert electrical energy into kinetic energy using the motor effect, while generators and transformers rely on electromagnetic induction to convert kinetic energy into electrical energy. This chapter covers the principles, rules, and examinable applications you need for the Edexcel IGCSE Physics syllabus.

电动机与电磁感应是同一枚硬币的两面：电动机利用“电动机效应”将电能转化为动能，而发电机和变压器则依靠电磁感应将动能转化为电能。本章将涵盖 Edexcel IGCSE 物理考纲中要求掌握的原理、定则及应用。

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1. The Motor Effect | 电动机效应

When a conductor carrying an electric current is placed in a magnetic field, it experiences a force. This phenomenon is called the motor effect. The force arises because the magnetic field of the current-carrying wire interacts with the external magnetic field, producing a resultant field that pushes the wire sideways.

当一根通有电流的导体放置在磁场中时，它会受到一个力的作用。这一现象称为电动机效应。该力产生的原因是载流导线自身的磁场与外磁场相互作用，形成合磁场，从而将导线推向一侧。

For the force to be maximised, the conductor should be placed perpendicular (at 90°) to the magnetic field lines. If the conductor is parallel to the field, no force is exerted.

为了使力达到最大值，导体应垂直于磁场线放置（即成90°角）。如果导体与磁场平行，则不会受到力。

F = B I L

Where F is the force in newtons (N), B is the magnetic flux density in teslas (T), I is the current in amperes (A), and L is the length of the conductor in the magnetic field in metres (m).

其中 F 为力，单位牛顿（N）；B 为磁通量密度，单位特斯拉（T）；I 为电流，单位安培（A）；L 为导体在磁场中的长度，单位米（m）。

• The force is always perpendicular to both the magnetic field and the current direction.
• Reversing the current direction reverses the force direction.
• Reversing the magnetic field direction also reverses the force direction.
• Increasing B, I, or L increases the force proportionally.

• 力的方向始终同时垂直于磁场方向和电流方向。
• 反向电流会使力的方向反转。
• 反向磁场同样会使力的方向反转。
• 增大 B、I 或 L 都会使力成比例增大。

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2. Fleming’s Left-Hand Rule | 弗莱明左手定则

To determine the direction of the force, we use Fleming’s Left-Hand Rule. Hold the thumb, first finger, and second finger of your left hand so that they are mutually at right angles:

为了判断力的方向，我们使用弗莱明左手定则。将左手的大拇指、食指和中指两两垂直放置：

Finger	Direction	Chinese
ThuMb → M	Force / Motion	大拇指 → 力/运动方向
First finger → F	Field (N → S)	食指 → 磁场方向（N → S）
SeCond finger → C	Current (⁺ → ⁻)	中指 → 电流方向（⁺ → ⁻）

A common mnemonic is “FBI”: Force (thumb), Field (first finger), Current (second finger) — remembering that the first finger follows Field, and the second finger follows Current alphabetically.

一个常用的记忆口诀是“FBI”：力（拇指）、磁场（食指）、电流（中指）——食指对应 Field（磁场），中指对应 Current（电流），首字母按字母顺序排列。

In exam questions, always draw the magnetic field lines first (N to S), then mark the current direction, and finally apply the left-hand rule to find the direction of motion or force.

在考试中，应先画出磁场线（从N极到S极），再标出电流方向，最后用左手定则判定运动或力的方向。

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3. Factors Affecting the Force | 影响力的因素

From the equation F = B I L, three key factors determine the magnitude of the force on a current-carrying conductor in a magnetic field:

根据公式 F = B I L，决定磁场中载流导体受力大小的三个关键因素是：

Factor | 因素	Effect on Force | 对力的影响
Magnetic flux density B | 磁通量密度 B	Stronger magnet → larger force | 磁体越强，力越大
Current I | 电流 I	Larger current → larger force | 电流越大，力越大
Length of conductor L | 导体有效长度 L	Longer wire in field → larger force | 磁场中导线越长，力越大
Angle θ | 角度 θ	Force is maximum at 90°, zero at 0° | 90°时力最大，0°时力为零

In practice, electric motors increase the turning effect by using a coil with many turns and by placing the coil inside a radial magnetic field using curved pole pieces.

在实际电动机中，为了增大转动力矩，会使用多匝线圈，并通过弯曲的磁极片使线圈处于辐射状磁场中。

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4. Construction of a Simple Electric Motor | 简易电动机的结构

A simple DC motor consists of the following key parts:

简易直流电动机由以下关键部件构成：

• Coil (armature): a rectangular coil of wire that rotates.
• Magnets: provide the external magnetic field (usually two permanent magnets or electromagnets).
• Commutator: a split ring that reverses the current direction every half turn.
• Brushes: carbon contacts that supply current to the rotating coil.
• Axle: the central rod on which the coil rotates.

• 线圈（电枢）：一个可旋转的矩形导线线圈。
• 磁体：提供外部磁场（通常为两个永磁体或电磁铁）。
• 换向器：一个半环（裂环），每半圈反转一次电流方向。
• 电刷：碳质触点，向旋转线圈输送电流。
• 转轴：线圈绕其旋转的中心轴。

Coil → Commutator → Brushes → External Circuit

线圈 → 换向器 → 电刷 → 外电路

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5. How the Motor Works | 电动机的工作原理

When current flows through the coil, one side of the coil experiences a force upward and the opposite side experiences a force downward, creating a couple (turning effect) that rotates the coil.

当电流通过线圈时，线圈的一侧受到向上的力，另一侧受到向下的力，形成力偶（转动力矩），使线圈旋转。

Step-by-step operation:

工作步骤：

Step 1: Current enters the coil through the brushes and commutator. Using Fleming’s Left-Hand Rule, one side of the coil is pushed up and the other side is pushed down, causing the coil to rotate.

第一步：电流通过电刷和换向器流入线圈。根据弗莱明左手定则，线圈一侧被向上推，另一侧被向下推，线圈开始旋转。

Step 2: As the coil reaches the vertical position, it is momentarily perpendicular to the magnetic field — the force on each side acts directly through the axis, producing zero turning moment. This is called the “dead point”.

第二步：当线圈转到竖直位置时，它暂时与磁场垂直——两侧的力恰好通过转轴作用，转动力矩为零。这称为“死点”。

Step 3: At this instant, the split-ring commutator changes contact from one brush to the other, reversing the current in the coil. This ensures that the force direction reverses, so the coil continues rotating in the same direction rather than reversing back.

第三步：在这一瞬间，裂环换向器从一个电刷切换到另一个电刷，使线圈中的电流反向。这样就保证了力的方向反转，从而使线圈继续沿同一方向旋转，而不是反向倒转。

Without the commutator, the coil would oscillate back and forth and stop at the vertical position. The commutator is therefore essential for continuous rotation in a DC motor.

如果没有换向器，线圈会在竖直位置附近来回摆动并最终停下。因此，换向器对于直流电动机的持续旋转至关重要。

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6. Electromagnetic Induction | 电磁感应

Electromagnetic induction is the production of an electromotive force (e.m.f.) across a conductor when it experiences a change in magnetic flux. This principle was discovered by Michael Faraday in 1831.

电磁感应是指当导体经历磁通量变化时，在导体两端产生电动势（e.m.f.）的现象。这一原理由迈克尔·法拉第于1831年发现。

An e.m.f. is induced in the following situations:

在以下情况下会感应出电动势：

• Moving a magnet into or out of a coil of wire.
• Moving a conductor through a magnetic field (e.g., a wire swept between poles of a magnet).
• Changing the current in a nearby coil (as in a transformer’s primary coil).

• 将磁体插入或拔出线圈。
• 使导体在磁场中运动（例如在磁极间扫动导线）。
• 改变附近线圈中的电流（如变压器初级线圈中的情况）。

The induced current flows only while the magnetic flux is changing. If the magnet stops moving, the current stops flowing.

感应电流仅在磁通量变化时存在。如果磁体停止运动，电流随即消失。

Induced e.m.f. ∝ rate of change of magnetic flux

感应电动势 ∝ 磁通量变化率

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7. Factors Affecting the Induced e.m.f. | 影响感应电动势的因素

Four main factors determine the magnitude of the induced e.m.f.:

决定感应电动势大小的四个主要因素：

Factor | 因素	Effect | 影响
Speed of motion | 运动速度	Faster movement → larger e.m.f. | 运动越快，感应电动势越大
Magnetic field strength | 磁场强度	Stronger magnet → larger e.m.f. | 磁体越强，感应电动势越大
Number of turns on the coil | 线圈匝数	More turns → larger e.m.f. | 匝数越多，感应电动势越大
Area of the coil | 线圈面积	Larger area → larger e.m.f. | 面积越大，感应电动势越大

This is quantified by Faraday’s Law: the induced e.m.f. is proportional to the rate at which the magnetic flux linkage is cut by the conductor.

这由法拉第定律量化描述：感应电动势与导体切割磁链的速率成正比。

To reverse the direction of the induced current, either move the magnet in the opposite direction, or flip the magnet’s poles (use the opposite pole).

要使感应电流方向反转，可以反向移动磁体，或翻转磁体磁极（使用相反的磁极）。

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8. Lenz’s Law | 楞次定律

Lenz’s Law states that the direction of an induced current is always such that it opposes the change that produced it. This is a consequence of the conservation of energy — the induced current creates a magnetic field that resists the motion of the magnet.

楞次定律指出：感应电流的方向总是阻碍引起它的变化。这是能量守恒定律的必然结果——感应电流产生的磁场会抵抗磁体的运动。

Practical interpretation:

实际理解：

• If you push a north pole of a magnet into a coil, the coil’s near face becomes a north pole, repelling the magnet.
• If you pull the north pole out of the coil, the coil’s near face becomes a south pole, attracting the magnet.
• Thus, work must be done to move the magnet against this opposing force — this work is converted into electrical energy.

• 当把磁体N极插入线圈时，线圈靠近磁体的一端变为N极，排斥磁体。
• 当把N极从线圈中拔出时，线圈靠近磁体的一端变为S极，吸引磁体。
• 因此，必须克服这一阻碍力做功——这些功转化为电能。

In exam questions, you may be asked to determine the direction of the induced current. Use Lenz’s Law to identify the polarity of the induced magnetic field, then apply the right-hand grip rule to find the current direction in the coil.

在考试中，可能会要求你判断感应电流的方向。先用楞次定律确定感应磁场的方向，再用右手螺旋定则（安培定则）判断线圈中的电流方向。

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9. Generators: AC and DC | 发电机：交流与直流

A generator is the reverse of a motor — it converts kinetic energy into electrical energy using electromagnetic induction. When a coil is rotated in a magnetic field, the magnetic flux through the coil changes continuously, inducing an alternating e.m.f.

发电机是电动机的逆过程——它利用电磁感应将动能转化为电能。当线圈在磁场中旋转时，穿过线圈的磁通量不断变化，从而感应出交变电动势。

Feature | 特征	AC Generator | 交流发电机	DC Generator | 直流发电机
Output | 输出	Alternating current | 交变电流	Direct current (pulsating) | 直流（脉动）
Connecting device | 连接装置	Slip rings + brushes | 滑环 + 电刷	Split-ring commutator + brushes | 裂环换向器 + 电刷
e.m.f. waveform | 电动势波形	Sinusoidal (alternates sign) | 正弦波形（正负交替）	Always positive, varies in magnitude | 始终为正，大小脉动

The output of a simple AC generator is a sine wave. The e.m.f. is zero when the coil is perpendicular to the field (maximum flux, zero rate of change) and maximum when the coil is parallel to the field (zero flux, maximum rate of change).

简单交流发电机的输出为正弦波。当线圈垂直于磁场时（磁通量最大、变化率为零），电动势为零；当线圈平行于磁场时（磁通量为零、变化率最大），电动势达到最大值。

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10. Transformers | 变压器

A transformer uses electromagnetic induction to change the voltage of an alternating current. It consists of two coils (primary and secondary) wound around a soft iron core.

变压器利用电磁感应改变交流电的电压。它由一个软铁芯和绕在铁芯上的两个线圈（初级线圈和次级线圈）组成。

How it works:

工作原理：

• An alternating current in the primary coil produces a continuously changing magnetic field in the iron core.
• This changing magnetic flux passes through the secondary coil, inducing an alternating e.m.f. across it.
• The ratio of voltages equals the ratio of turns: Vₚ / Vₛ = Nₚ / Nₛ.

• 初级线圈中的交流电在铁芯中产生持续变化的磁场。
• 这一变化的磁通量穿过次级线圈，在其两端感应出交变电动势。
• 电压之比等于匝数之比：Vₚ / Vₛ = Nₚ / Nₛ。

Vₚ / Vₛ = Nₚ / Nₛ

A step-up transformer has Nₛ > Nₚ and increases the voltage; a step-down transformer has Nₛ < Nₚ and decreases the voltage. For an ideal transformer with 100% efficiency:

升压变压器的Nₛ > Nₚ，使电压升高；降压变压器的Nₛ < Nₚ，使电压降低。对于效率为100%的理想变压器：

Vₚ Iₚ = Vₛ Iₛ   (power in = power out)

Vₚ Iₚ = Vₛ Iₛ  （输入功率 = 输出功率）

Transformers only operate with alternating current. A direct current would produce a steady magnetic field, causing no change in flux and hence no induced e.m.f. in the secondary coil.

变压器只能使用交流电工作。直流电产生恒定磁场，磁通量不变化，次级线圈中无法感应出电动势。

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11. Energy Losses in Transformers | 变压器中的能量损耗

Real transformers are not perfectly efficient. Energy is lost through several mechanisms:

实际变压器并非100%高效，能量损失主要通过以下几种途径：

Cause | 原因	Remedy | 解决方法
Heating of coils (I²R loss) | 线圈发热（I²R 损耗）	Use thick, low-resistance copper wire | 使用粗的低电阻铜线
Eddy currents in the core | 铁芯中的涡流	Use a laminated (layered) iron core | 使用叠片（分层）铁芯
Magnetisation/reversal of core | 铁芯反复磁化/退磁	Use soft iron with low hysteresis | 使用磁滞损耗低的软铁
Flux leakage | 磁通泄漏	Wind both coils on the same closed iron core | 将两线圈绕在同一闭合铁芯上

In the national grid, transformers step voltage up to very high values (e.g., 400 kV) for transmission, which reduces the current and therefore dramatically reduces the I²R power loss in the cables.

在国家电网中，输电前用变压器将电压升至很高（如400 kV），这样电流大幅减小，从而显著降低输电线上的 I²R 功率损耗。

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

Here are the most frequently tested points and pitfalls in Edexcel IGCSE Physics:

以下是 Edexcel IGCSE 物理考试中最常考的知识点及易错点：

• Left hand for motors, right hand for generators. Fleming’s Left-Hand Rule is for the motor effect (force on a current-carrying conductor); Fleming’s Right-Hand Rule is for electromagnetic induction (induced current direction).
• Do not confuse the commutator (split ring, used in DC motors/DC generators) with slip rings (used in AC generators).
• Remember that a transformer only works with AC, never DC.
• When calculating transformer ratios, ensure you correctly identify the primary and secondary coils.
• “Induced current opposes the motion” — quote Lenz’s Law explicitly in longer answer questions.

• 电动机用左手，发电机用右手。弗莱明左手定则用于电动机效应（载流导体受力）；弗莱明右手定则用于电磁感应（感应电流方向）。
• 不要混淆换向器（裂环，用于直流电动机/直流发电机）与滑环（用于交流发电机）。
• 记住：变压器只能用交流电，绝不能用直流电。
• 计算变压器匝数比时，注意正确区分初级线圈与次级线圈。
• “感应电流阻碍运动”——回答长答题时务必明确引用楞次定律。

Finally, always apply a systematic approach to motor/generator problems: identify the direction of the magnetic field → identify the direction of current or motion → apply the correct hand rule → state the direction of force or induced current.

最后，解决电动机/发电机问题时应采用系统化思路：先确定磁场方向 → 再确定电流方向或运动方向 → 应用正确的定则 → 判断力的方向或感应电流方向。

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