Observing Induction | 观察电磁感应

📚 Observing Induction | 观察电磁感应

Electromagnetic induction is the production of an electromotive force (emf) across a conductor when it experiences a changing magnetic flux. In CIE A Level Physics, you are expected not only to calculate induced emf but also to describe and interpret observations from induction experiments.

电磁感应是导体在经历变化的磁通量时产生电动势（emf）的过程。在 CIE A Level 物理中，你不仅要会计算感应电动势，还要能描述并解释电磁感应实验中的观察现象。

1. What is electromagnetic induction? | 什么是电磁感应

Electromagnetic induction occurs whenever the magnetic flux linking a circuit changes. The induced emf can drive an induced current if the circuit is closed. No battery is required; mechanical energy is converted into electrical energy.

每当穿过电路的磁通量发生变化时，就会发生电磁感应。若电路闭合，感应电动势会驱动感应电流。这一过程不需要电池，机械能被转化为电能。

Observationally, induction is often shown by moving a magnet near a coil or by moving a conductor through a magnetic field. The key condition is relative motion or a changing field, not a steady magnetic field.

从观察角度看，通常通过让磁铁靠近或远离线圈、或让导体在磁场中运动来演示感应现象。关键条件是相对运动或变化的磁场，而不是恒定的磁场。

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2. Magnetic flux and flux linkage | 磁通量与磁链

Magnetic flux Φ is defined as Φ = B A cos θ, where B is the magnetic flux density, A is the area, and θ is the angle between the magnetic field and the normal to the area. The SI unit is the weber (Wb).

磁通量 Φ 定义为 Φ = B A cos θ，其中 B 是磁通密度，A 是面积，θ 是磁场方向与面积法线之间的夹角。其 SI 单位是韦伯（Wb）。

For a coil with N turns, the magnetic flux linkage is NΦ. In experiments, increasing the number of turns increases the induced emf because more flux is linked.

对于匝数为 N 的线圈，磁链为 NΦ。在实验中，增加线圈匝数会增大感应电动势，因为有更多的磁通量被链住。

Φ = B A cos θ

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3. Faraday’s law of induction | 法拉第电磁感应定律

Faraday’s law states that the induced emf in a circuit is directly proportional to the rate of change of magnetic flux linkage. For a coil of N turns, the average induced emf is given by:

法拉第电磁感应定律指出，电路中的感应电动势与磁链的变化率成正比。对于匝数为 N 的线圈，平均感应电动势由下式给出：

ε = -N ΔΦ / Δt

The negative sign indicates the direction of the induced emf and is associated with Lenz’s law. In observations, a faster change in flux produces a larger deflection on a galvanometer.

负号表示感应电动势的方向，它与楞次定律相关。在观察中，磁通量变化越快，检流计的偏转越大。

If the flux change is not uniform, the instantaneous emf is proportional to the gradient of a flux-time graph. CIE questions often ask you to interpret graphs of Φ against t.

如果磁通量变化不均匀，瞬时电动势正比于磁通量-时间图像的斜率。CIE 考题常要求解释 Φ 对 t 的图像。

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4. Lenz’s law and the negative sign | 楞次定律与负号

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 consequence of conservation of energy.

楞次定律指出，感应电流的方向总是使它阻碍产生它的磁通量变化。这是能量守恒的结果。

Observationally, when a north pole approaches a coil, the coil develops a face that is also north, repelling the magnet. When the magnet is withdrawn, the coil face becomes south, attracting the magnet. This opposition can be felt as a resisting force.

从观察上看，当磁铁 N 极靠近线圈时，线圈靠近磁铁的一端也形成 N 极，排斥磁铁；当磁铁退出时，该端变为 S 极，吸引磁铁。你可以感受到这种阻碍作用表现为阻力。

Thus, mechanical work must be done to move the magnet. Without Lenz’s law, energy would be created from nothing, which is impossible.

因此，移动磁铁必须做功。若没有楞次定律，能量就会凭空产生，这是不可能的。

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5. Demonstrating induction with a magnet and coil | 用磁铁和线圈演示感应

A classic observation uses a bar magnet, a solenoid connected to a centre-zero galvanometer, and connecting wires. When the magnet is pushed into the coil, the galvanometer pointer deflects in one direction.

经典演示使用条形磁铁、连接中心零位检流计的螺线管和导线。当磁铁推入线圈时，检流计指针向一个方向偏转。

When the magnet is held stationary inside the coil, the pointer returns to zero, showing no induced emf. When the magnet is pulled out, the pointer deflects in the opposite direction.

当磁铁在线圈内保持静止时，指针回到零位，表明没有感应电动势。当磁铁被拉出时，指针向相反方向偏转。

If the magnet is moved faster, the deflection is larger. This shows that induced emf depends on the rate of change of flux, not the total flux itself.

如果磁铁移动更快，偏转就更大。这说明感应电动势取决于磁通量的变化率，而不是磁通量本身的大小。

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6. Observing induced EMF with a galvanometer | 用检流计观察感应电动势

A centre-zero galvanometer is ideal for observing induction because it indicates both magnitude and direction of a small current. The direction of deflection shows the polarity of the induced emf.

中心零位检流计非常适合观察感应现象，因为它能显示微小电流的大小和方向。偏转方向表明感应电动势的极性。

In an experiment, repeating the motion with reversed magnet polarity reverses the deflection. Likewise, moving the coil towards a stationary magnet produces the same effect as moving the magnet towards the coil.

在实验中，将磁铁极性反转后再重复运动，指针偏转方向也会反转。同样，让线圈向静止磁铁运动，与让磁铁向线圈运动产生的效果相同。

Only relative motion matters. These observations support the idea that induction arises from a changing flux linkage, not from the mere presence of a magnetic field.

只有相对运动才是关键。这些观察支持一个观点：感应源于变化的磁链，而不仅仅是磁场的存在。

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7. Induction in a straight conductor | 直导线中的感应

When a straight conductor of length L moves with speed v across a uniform magnetic field B, an emf is induced across its ends. If the motion is perpendicular to the field, the induced emf is:

当长度为 L 的直导线以速度 v 在均匀磁场 B 中运动时，其两端会产生感应电动势。若运动方向与磁场垂直，感应电动势为：

ε = B L v sin θ

Here θ is the angle between the velocity and the magnetic field. Observations show that moving the conductor parallel to the field lines produces no emf, which corresponds to sin 0° = 0.

其中 θ 是速度与磁场方向之间的夹角。观察表明，导体平行于磁感线运动时不会产生电动势，这对应于 sin 0° = 0。

This effect can be demonstrated by connecting a conducting wire or rod to a galvanometer and sweeping it through the field of a large horseshoe magnet. The faster the sweep, the greater the galvanometer deflection.

该效应可以通过将导线或金属棒连接到检流计，并在大型马蹄形磁铁磁场中摆动来演示。摆动越快，检流计偏转越大。

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8. Eddy currents and their observation | 涡流及其观察

Eddy currents are circulating currents induced in a solid conductor when it experiences a changing magnetic flux. They can be observed as a braking force on a metal pendulum swinging between magnet poles.

涡流是当块状导体经历变化的磁通量时，在导体内产生的环流。它们可以通过金属摆在磁极间摆动时受到的制动作用来观察。

A common demonstration uses a copper or aluminium plate swinging through a strong magnetic field. The plate slows rapidly because eddy currents create magnetic fields that oppose the motion, in accordance with Lenz’s law.

常见演示是让铜板或铝板在强磁场中摆动。板会迅速减速，因为涡流产生的磁场按照楞次定律阻碍运动。

If slits are cut in the plate, the eddy current paths are broken, and the damping is much weaker. This is clear observational evidence that

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