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 (emf) in a conductor. It is the foundation of generators, transformers, induction chargers and many other technologies. In CIE A-Level Physics, you are expected to apply Faraday’s law and Lenz’s law quantitatively and explain energy transfer in inductive systems.

电磁感应是指变化的磁通量在导体中产生电动势的过程。它是发电机、变压器、感应充电等许多技术的基础。在 CIE A-Level 物理中，你需要定量应用法拉第定律和楞次定律，并解释感应系统中的能量转换。

1. 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. For a uniform field of strength B making an angle θ with the normal to area A, the flux is given by Φ = B A cos θ. Its SI unit is the weber (Wb), where 1 Wb = 1 T m².

磁通量 Φ 是穿过某一面积的磁场总量的量度。若匀强磁场 B 与面积 A 的法线成 θ 角，则磁通量为 Φ = B A cos θ。其国际单位是韦伯 Wb，1 Wb = 1 T m²。

When a coil has N turns, the total flux linked with the coil is NΦ. This quantity is called flux linkage and is measured in weber-turns. Maximum flux occurs when the field is perpendicular to the plane (θ = 0); when the plane is parallel to the field, flux is zero.

当线圈有 N 匝时，与线圈交链的总磁通为 NΦ。这个量称为磁链，单位是韦伯-匝。当磁场垂直于线圈平面时 θ = 0，磁通最大；当线圈平面平行于磁场时，磁通为零。

Φ = B A cos θ

Flux linkage = NΦ

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 emf in a circuit is directly proportional to the rate of change of magnetic flux linkage. For an average change over time Δt, the induced emf is ε = Δ(NΦ)/Δt. The instantaneous emf is obtained when Δt tends to zero.

法拉第定律指出，回路中感应电动势的大小与磁链的变化率成正比。对于一段时间 Δt 内的平均变化，感应电动势为 ε = Δ(NΦ)/Δt。当 Δt 趋近于零时，得到瞬时电动势。

An emf can be induced by changing the magnetic field strength, changing the area of the coil, or changing the angle between the coil and the field. In all cases, only the change in flux matters, not the absolute value of flux.

通过改变磁场强度、改变线圈面积或改变线圈与磁场之间的角度，都可以感应出电动势。在所有情况下，只有磁通量的变化才起作用，磁通量的绝对值并不重要。

ε = Δ(NΦ) / Δt

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 produces it. This is represented by the negative sign in Faraday’s law: ε = – Δ(NΦ)/Δt. The opposition ensures that energy is transferred rather than created from nothing.

楞次定律指出，感应电流的方向总是阻碍产生它的磁通量变化。这体现在法拉第定律中的负号：ε = – Δ(NΦ)/Δt。这种阻碍作用保证了能量只是被转化，而不是凭空产生。

For example, when a north pole of a magnet approaches a coil, the induced current creates a north pole on the near face to repel the 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，以排斥磁铁。外力必须克服这种排斥做功，机械功由此转化为电能。

If the induced current aided the change, a small initial movement would produce more current, which would produce more movement, violating energy conservation and creating a perpetual motion effect.

如果感应电流帮助磁通变化，那么一个微小的初始运动就会产生更多电流，进而产生更多运动，这违背能量守恒并形成永动机效应。

4. Induced EMF in a Moving Conductor | 直导线切割磁感线的感应电动势

A straight conductor of length l moving with speed v perpendicular to a magnetic field B sweeps out an area of l v per second. The flux cut per second is

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