AS Physics: Electromagnetic Induction - Key Concepts | AS 物理：电磁感应考点精讲

📚 AS Physics: Electromagnetic Induction – Key Concepts | AS 物理：电磁感应考点精讲

Electromagnetic induction is the production of an electromotive force (emf) across a conductor when it is exposed to a varying magnetic field. This principle underpins generators, transformers, and almost all modern electrical technology. In AS Physics, you need to grasp magnetic flux, Faraday’s law, Lenz’s law, and their practical applications.

电磁感应是指当导体处于变化的磁场中时，导体两端产生电动势（emf）的现象。发电、变电和几乎所有现代电力技术都基于这一原理。在 AS 物理中，你需要掌握磁通量、法拉第定律、楞次定律及其实际应用。

1. Magnetic Flux | 磁通量

Magnetic flux Φ through a surface area A is defined as Φ = BA cos θ, where B is the magnetic flux density (in teslas), A is the area (in m²), and θ is the angle between the magnetic field lines and the normal to the surface. The unit of flux is the weber (Wb).

磁通量 Φ 定义为穿过面积 A 的磁感线总数：Φ = BA cos θ，其中 B 为磁通密度（单位特斯拉），A 为面积（m²），θ 为磁场方向与面积法线之间的夹角。磁通量的单位是韦伯（Wb）。

When the field is perpendicular to the surface (θ = 0), flux is maximum: Φ = BA. When the field is parallel to the surface (θ = 90°), flux is zero because no field lines pass through.

当磁场垂直于表面（θ = 0）时，磁通量最大：Φ = BA。当磁场与表面平行（θ = 90°）时，磁通量为零，因为没有磁感线穿过。

2. Changing Magnetic Flux | 磁通量的变化

An emf is induced only when the magnetic flux linking a circuit changes. Flux can change by varying B, varying A, varying θ, or any combination of these. The key is the rate of change, not the absolute value of flux.

只有当穿过回路的磁通量 发生变化 时，才会产生感应电动势。磁通量可通过改变 B、改变 A、改变 θ 或它们的组合而变化。关键是变化率，而非磁通量的绝对值。

Moving a magnet towards or away from a coil (changes B).
Moving a coil towards or away from a magnetic field (changes B).
Rotating a coil in a magnetic field (changes θ).
Changing the area of a coil inside a field (changes A).

磁铁靠近或远离线圈（改变 B）。
线圈靠近或远离磁场（改变 B）。
线圈在磁场中旋转（改变 θ）。
改变磁场内线圈的面积（改变 A）。

3. 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 emf ℰ in a circuit is equal to the rate of change of magnetic flux linkage through the circuit.

法拉第定律指出，回路中产生的感应电动势 ℰ 的大小等于穿过该回路的磁链变化率。

ℰ = – ΔΦ / Δt (for average emf) or ℰ = – dΦ/dt (instantaneous)

ℰ = – ΔΦ / Δt （平均电动势）或 ℰ = – dΦ/dt （瞬时电动势）

For a coil of N turns, the flux linkage is NΦ, so the induced emf becomes:

对于 N 匝线圈，磁链为 NΦ，感应电动势变为：

ℰ = – N (ΔΦ / Δt)

The negative sign relates to Lenz’s law, which we will discuss next. The unit of emf is the volt (V).

负号与楞次定律有关，下面会讨论。电动势的单位是伏特（V）。

4. Lenz’s Law | 楞次定律

Lenz’s law gives the direction of the induced emf and current: the induced current flows in a direction such that it opposes the change in magnetic flux that produced it. This is a consequence of the conservation of energy.

楞次定律给出了感应电动势和电流的方向：感应电流的方向总是使它产生的磁场阻碍引起感应电流的磁通量的变化。这是能量守恒的结果。

If a north pole of a magnet approaches a coil, the induced current creates a north pole on the coil side facing the magnet to repel it (opposing the approach). If the magnet is withdrawn, the coil creates a south pole to attract (opposing the withdrawal).

如果磁铁的 N 极靠近线圈，感应电流使线圈朝向磁铁的一端形成 N 极，以排斥磁铁（阻碍靠近）。若磁铁被抽走，线圈则形成 S 极以吸引磁铁（阻碍远离）。

You can determine the current direction using the right-hand grip rule for solenoids. Always remember: the induced current opposes the change, not the flux itself.

可用螺线管的右手螺旋定则判断电流方向。务必记住：感应电流阻碍的是磁通量的变化，而非磁通量本身。

5. Motional EMF | 动生电动势

When a straight conductor of length L moves with velocity v perpendicular to a uniform magnetic field B, an emf is induced across its ends. This is called motional emf, given by:

当长度为 L 的直导体以速度 v 垂直于匀强磁场 B 运动时，导体两端产生电动势，称为动生电动势：

ℰ = B L v

This is derived from cutting magnetic flux lines. If the velocity makes an angle θ with the field, the component perpendicular to B is v sin θ, so ℰ = B L v sin θ.

该公式源于切割磁感线。若速度与磁场夹角为 θ，则垂直分量为 v sin θ，因此 ℰ = B L v sin θ。

Using Fleming’s right-hand rule (for generators), point thumb in the direction of motion, forefinger in the direction of field, then middle finger gives the direction of induced conventional current (from negative to positive terminal).

使用弗莱明右手定则（发电机定则）：拇指指向运动方向，食指指向磁场方向，中指指示感应电流（正电荷移动方向，即从负极到正极）。

6. AC Generator | 交流发电机

A simple AC generator consists of a rectangular coil rotating in a uniform magnetic field. As the coil rotates, the flux linkage changes sinusoidally, producing an alternating emf.

简单的交流发电机由在匀强磁场中旋转的矩形线圈构成。线圈旋转时，磁链按正弦规律变化，产生交变电动势。

The emf at any time t is: ℰ = N B A ω sin(ωt), where ω is the angular speed. Peak emf ℰ₀ = N B A ω.

任意时刻 t 的电动势：ℰ = N B A ω sin(ωt)，其中 ω 为角速度。峰值电动势 ℰ₀ = N B A ω。

The frequency of the alternating emf is equal to the rotational frequency. Slip rings and brushes ensure continuous electrical connection without tangling wires. The output is a sinusoidal waveform.

交变电动势的频率等于旋转频率。滑环和电刷保证电路持续连接而导线不打结。输出为正弦波形。

7. Transformers | 变压器

An ideal transformer operates on the principle of mutual induction. An alternating current in the primary coil produces a changing magnetic flux, which links the secondary coil and induces an emf.

理想变压器基于互感原理工作。初级线圈中的交流电流产生变化的磁通量，该磁通量穿过次级线圈，产生感应电动势。

The turns ratio equation:

Vₚ / Vₛ = Nₚ / Nₛ

For an ideal (100% efficient) transformer, power input = power output: Pₚ = Pₛ, so Vₚ Iₚ = Vₛ Iₛ. Thus:

对于理想（100% 效率）变压器，输入功率 = 输出功率：Pₚ = Pₛ，因此 Vₚ Iₚ = Vₛ Iₛ，得到：

Iₚ / Iₛ = Nₛ / Nₚ

Step-up transformers increase voltage and decrease current; step-down transformers do the opposite. Real transformers have energy losses due to eddy currents, hysteresis, and coil resistance.

升压变压器升高电压、降低电流；降压变压器则相反。实际变压器因涡流、磁滞和线圈电阻存在能量损失。

8. Eddy Currents | 涡流

Eddy currents are induced circulating currents in a bulk conductor exposed to a changing magnetic field. They oppose the change in flux (Lenz’s law) and cause heating and braking effects.

涡流是在块状导体内因变化的磁场而产生的感应环流。它们反抗磁通量的变化（楞次定律），并产生热效应和制动效应。

In transformers, eddy currents are minimized by laminating the iron core – thin insulated sheets of iron restrict the paths for eddy currents, reducing energy loss.

在变压器中，通过使用叠片铁芯来减小涡流——绝缘薄铁片限制了涡流的路径，从而降低能量损失。

Eddy currents are useful in electromagnetic braking (e.g., in trains and roller coasters) and induction heating (e.g., induction cookers).

涡流可用于电磁制动（如火车和过山车）以及感应加热（如电磁炉）。

9. Energy Conservation in Electromagnetic Induction | 电磁感应中的能量守恒

Lenz’s law is a direct consequence of energy conservation. If the induced current aided the change in flux, a small movement would produce more current, which would aid more movement – a runaway energy creation, which is impossible.

楞次定律是能量守恒的直接体现。假如感应电流帮助磁通量的变化，微小的运动会产生更大的电流，进而助推更强的运动——能量会无中生有，这是不可能的。

For example, when a magnet falls through a conducting tube, eddy currents create an upward magnetic force opposing the fall, causing the magnet to descend slowly. The lost gravitational potential energy is converted into electrical energy and then heat.

例如，当磁铁在金属管中下落时，涡流产生向上的磁场力阻碍下落，使磁铁缓慢下落。减少的重力势能转化为电能，继而变为热能。

10. Graphs and Graphical Analysis | 图像与图像分析

You must be able to sketch and interpret graphs of flux Φ versus time, and induced emf ℰ versus time for various scenarios. The induced emf is the negative gradient of the flux–time graph: ℰ = – dΦ/dt.

你必须能够绘制并解读不同情况下磁通量 Φ–t 图和感应电动势 ℰ–t 图。感应电动势等于磁通量–时间图线的负斜率：ℰ = – dΦ/dt。

Scenario / 情景	Φ shape / 形状	ℰ shape / 形状
Magnet entering coil at steady speed 磁铁匀速进入线圈	Increasing linearly / 线性增加	Constant positive (then negative when leaving) / 匀速进入时常量正，离开时常量负
Coil rotating uniformly in field 线圈在磁场中匀速旋转	Cosine wave / 余弦波	Sine wave (shifted) / 正弦波（有相位差）
Triangular B–field variation 三角形 B 场变化	Triangle wave / 三角波	Square wave (derivative of triangle) / 方波

Peak emf occurs when the flux is zero but changing most rapidly (for sinusoidal flux). Emf is zero when flux is maximum/minimum (zero rate of change).

对于正弦变化的磁通量，峰值电动势出现在磁通量为零但变化最快时。磁通量最大或最小时电动势为零（变化率为零）。

11. Common Misconceptions | 常见误区

“Induced current flows to oppose the magnetic field.” Actually it opposes the change in flux. A constant field produces no emf. / “感应电流阻碍磁场”。实际上它阻碍的是磁通量的变化。恒定磁场不产生电动势。
“Faraday’s law gives the current directly.” It gives the emf; current depends on circuit resistance. / “法拉第定律直接给出电流”。它给出的是电动势；电流取决于电阻。
“Fleming’s right-hand rule works for motors.” No, left-hand rule is for motor effect; right-hand rule is for generator effect. / “弗莱明右手定则用于电动机”。不，左手定则用于电动机效应；右手定则用于发电机效应。
“Step-up transformer creates energy.” It increases voltage but decreases current proportionally; power remains constant (ideal). / “升压变压器创造能量”。它升高电压但按比例减小电流；功率保持不变（理想情况）。

12. Exam Tips and Calculation Steps | 考试提示与计算步骤

When solving numerical problems, follow these steps:

解数值题时请遵循以下步骤：

Identify what is changing: B, A, θ – or identify the motion. / 确定什么在变化：B、A、θ——或确定运动方式。
Write the flux expression: Φ = BA cos θ or NΦ for a coil. / 写出磁通量表达式：Φ = BA cos θ，或对于线圈 NΦ。
Calculate the change in flux ΔΦ and the time interval Δt. / 计算磁通量变化 ΔΦ 和时间间隔 Δt。
Apply ℰ = – N (ΔΦ /Δt). Use negative sign only if direction is required. / 应用 ℰ = – N (ΔΦ /Δt)。仅在需要方向时使用负号。
For motional emf, check if the conductor cuts field lines perpendicularly: ℰ = B L v sin θ. / 对于动生电动势，检查导体是否垂直切割磁感线：ℰ = B L v sin θ。
For transformers, first apply turns ratio, then power equation. Remember ideal vs. real efficiency. / 对于变压器，先使用匝数比，再使用功率方程。牢记理想与实际效率的区别。

Always include units: B in T, A in m², Φ in Wb, v in m s⁻¹, L in m, emf in V. Practice graph interpretation: gradient of Φ–t is the emf magnitude.

始终注明单位：B 用 T，A 用 m²，Φ 用 Wb，v 用 m s⁻¹，L 用 m，电动势用 V。练习图像解读：Φ–t 图斜率即电动势大小。

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AS Physics: Electromagnetic Induction – Key Concepts | AS 物理：电磁感应 考点精讲