Electromagnetic Induction | 电磁感应

📚 Electromagnetic Induction | 电磁感应

Electromagnetic induction is the process by which a changing magnetic flux generates an electromotive force (e.m.f.) in a conductor. This topic underpins generators, transformers, induction charging, and many practical systems in the Edexcel A-Level Physics specification.

电磁感应是变化的磁通量在导体中产生电动势（e.m.f.）的过程。该主题是发电机、变压器、感应充电以及许多实际系统的基础，属于 Edexcel A-Level 物理考试的重要内容。

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

Magnetic flux Φ is a measure of the number of magnetic field lines passing through a given area. For a uniform field, the flux through a plane coil is Φ = BA cos θ, where B is the magnetic flux density in tesla (T), A is the area in square metres (m²), and θ is the angle between the field direction and the normal to the area.

磁通量 Φ 是穿过某一面积的磁感线数量的量度。对于匀强磁场，穿过平面线圈的磁通量为 Φ = BA cos θ，其中 B 为磁通密度（单位 T），A 为面积（单位 m²），θ 为磁场方向与面积法线之间的夹角。

Φ = BA cos θ

When the coil has N turns, the total flux linkage is NΦ = BAN cos θ. Flux linkage is the quantity that appears directly in Faraday’s law, so it is important to distinguish flux from flux linkage.

当线圈有 N 匝时，总磁链为 NΦ = BAN cos θ。磁链是法拉第定律中直接出现的物理量，因此区分磁通量与磁链非常重要。

Flux linkage = NΦ = BAN cos θ

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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. is equal to the rate of change of magnetic flux linkage. In symbols, the average induced e.m.f. is given by ε = N ΔΦ/Δt, where ΔΦ is the change in flux through one turn and Δt is the time taken for the change.

法拉第定律指出，感应电动势的大小等于磁链的变化率。用符号表示，平均感应电动势为 ε = N ΔΦ/Δt，其中 ΔΦ 是单匝线圈中磁通量的变化量，Δt 是变化所需的时间。

ε = −N ΔΦ / Δt

The minus sign is often included to show the direction of the induced e.m.f. as described by Lenz’s law. A faster change in flux linkage produces a larger induced e.m.f., even if the total flux change is the same.

公式中的负号通常用来表示楞次定律所描述的感应电动势方向。磁链变化越快，产生的感应电动势越大，即使总的磁通量变化相同。

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3. Lenz’s Law and Energy Conservation | 楞次定律与能量守恒

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 direct consequence of energy conservation: if the induced current assisted the change, energy would be created from nothing.

楞次定律指出，感应电流的方向总是使它产生的效果反抗引起感应电流的磁通量变化。这是能量守恒的直接结果：如果感应电流帮助磁通量变化，能量就会凭空产生。

For example, when a north pole of a magnet approaches a coil, the induced current creates a north pole at the near end of the coil to repel the incoming magnet. Work must be done against this repulsion, and that mechanical work is converted into electrical energy.

例如，当磁铁的 N 极靠近线圈时，感应电流使线圈靠近磁铁的一端形成 N 极，从而排斥靠近的磁铁。外力必须克服这种排斥做功，机械功因此转化为电能。

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4. Induced E.M.F. in a Moving Conductor | 运动导体中的感应电动势

When a straight conductor of length L moves with speed v perpendicular to a uniform magnetic field B, the induced e.m.f. across its ends is ε = BLv. This result can be derived by considering the area swept out by the conductor per unit time: the conductor cuts magnetic flux at a rate BLv.

当长度为 L 的直导体以速度 v 垂直于匀强磁场 B 运动时，导体两端产生的感应电动势为 ε = BLv。该结果可以通过考虑导体单位时间内扫过的面积来推导：导体切割磁通量的速率为 BLv。

ε = BLv

This equation is very useful for predicting the output of moving-conductor generators. The direction of the induced e.m.f. can be found from Fleming’s right-hand rule.

该公式在预测运动导体发电机的输出时非常有用。感应电动势的方向可以用弗莱明右手定则判断。

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5. Alternating Current Generators | 交流发电机

A coil rotating in a uniform magnetic field produces a sinusoidally varying e.m.f. The instantaneous induced e.m.f. is ε = BANω sin(ωt), where A is the coil area, N is the number of turns, ω is the angular speed, and t is time.

在匀强磁场中旋转的线圈会产生按正弦规律变化的电动势。瞬时感应电动势为 ε = BANω sin(ωt)，其中 A 为线圈面积，N 为匝数，ω 为角速度，t 为时间。

ε = BANω sin(ωt)

The peak e.m.f. is BANω. The frequency of the alternating e.m.f. is related to the angular speed by f = ω / 2π. The output graph is a sine wave, and the direction of the induced current reverses every half-cycle.

峰值电动势为 BANω。交流电动势的频率与角速度的关系为 f = ω / 2π。输出图像为正弦波形，感应电流的方向每半个周期反转一次。

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6. Transformers | 变压器

An ideal transformer consists of two coils wound on a laminated soft iron core. If the primary voltage is Vₚ and the secondary voltage is Vₛ, then Vₛ / Vₚ = Nₛ / Nₚ, where Nₚ and Nₛ are the numbers of turns on the primary and secondary coils.

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