← 返回资讯屏轩教育 · 行业资讯

Electromagnetic Induction | 电磁感应

2026-08-30 10:29 · 本文部分内容由AI辅助创作

📚 Electromagnetic Induction | 电磁感应

Electromagnetic induction is the process by which an electromotive force (EMF) is induced in a conductor when the magnetic flux through it changes. It is one of the most heavily tested topics in AQA International Physics A Unit 4 (PH04), appearing in both structured and extended-response questions.

电磁感应是指当穿过导体的磁通量发生变化时，在导体中产生电动势的过程。这是AQA国际A-Level物理第四单元（PH04）中最重要的考点之一，在结构题和解答题中均频繁出现。

1. Magnetic Flux and Flux Linkage | 磁通量与磁通匝连数

Magnetic flux Φ is defined as the product of the magnetic flux density B and the cross-sectional area A perpendicular to the field. When the plane of the coil makes an angle θ with the direction of the magnetic field, the flux is given by:

磁通量Φ定义为磁感应强度B与垂直于磁场的截面积A的乘积。当线圈平面的法线与磁场方向成角θ时，磁通量可以表示为：

Φ = BA cos θ

ge for a coil of N turns is defined as the product of the number of turns and the magnetic flux through each turn:

磁通量的单位是韦伯（Wb），即1 Wb = 1 T·m²。对于N匝线圈，磁通匝连数定义为匝数N与每匝磁通量Φ的乘积：

flux linkage = NΦ = BAN cos θ

2. Faraday's Law of Induction | 法拉第电磁感应定律

Faraday's law states that the magnitude of the induced EMF is directly proportional to the rate of change of flux linkage. The mathematical statement is:

法拉第定律指出：感应电动势的大小与磁通匝连数的变化率成正比。其数学表达式为：

EMF = −N dΦ/dt

The negative sign is the mathematical representation of Lenz's law, discussed in Section 3. When the flux changes uniformly over a time interval Δt, the average induced EMF is:

式中的负号是楞次定律的数学体现，将在第3节中详细讨论。当磁通量在时间间隔Δt内均匀变化时，平均感应电动势为：

EMF = −N ΔΦ/Δt

To increase the induced EMF, one can increase the rate of change of magnetic flux, increase the flux density, enlarge the coil area, or add more turns.

要增大感应电动势，可以增大磁通量的变化率、增大磁感应强度、增大线圈面积或增加线圈匝数。

3. Lenz's Law | 楞次定律

Lenz's law states that the direction of the induced current is such that it opposes the change that produced it. This principle follows directly from the conservation of energy: if the induced current reinforced the change, energy would be 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。这一原理直接源于能量守恒：如果感应电流促进磁通量的变化，能量就会凭空产生。

To determine the direction of the induced current, follow these steps:

判断感应电流方向时，可遵循以下步骤：

  1. Determine the direction of the external magnetic field.

  2. 判断外加磁场的方向。

  3. Decide whether the magnetic flux through the circuit is increasing or decreasing.

  4. 判断穿过回路的磁通量是增大还是减小。

  5. The induced current produces a magnetic field that opposes the change: if the flux is increasing, the induced field points against the external field; if the flux is decreasing, the induced field points in the same direction as the external field.

  6. 感应电流所产生的磁场阻碍这一变化：若磁通量增大，感应磁场方向与外加磁场相反；若磁通量减小，感应磁场方向与外加磁场相同。

4. Moving Conductor in a Magnetic Field | 磁场中运动的导体

When a conductor of length l moves at speed v perpendicular to a uniform magnetic field B, an EMF is induced across its ends. The magnitude of this motional EMF is:

当长度为l的导体以速度v垂直于匀强磁场B运动时，导体两端会产生感应电动势。这种动生电动势的大小为：

EMF = B l v

This can be derived by considering the magnetic force acting on charge carriers within the conductor. The work done per unit charge in separating the charges is equal to B l v.

该公式可以通过考虑导体内部载流子所受的磁力来推导。分离电荷所做的功每单位电荷即等于B·l·v。

If the conductor moves at an angle θ to the field, only the perpendicular component of velocity contributes:

若导体运动方向与磁场成角θ，则只有垂直于磁场的速度分量起作用：

EMF = B l v sin θ

广告 / Sponsored

牛津高阶英汉双解词典 第10版 商务印书馆
牛津高阶英汉双解词典 第10版 商务印书馆
¥168
📱 去京东购买
京东精选

5. AC Generator | 交流发电机

A simple AC generator consists of a rectangular coil of area A and N turns rotating at constant angular speed ω in a uniform magnetic field B. As the coil rotates, the flux linkage varies sinusoidally:

交流发电机由一个面积为A、匝数为N的矩形线圈在匀强磁场B中以恒定角速度ω旋转而成。当线圈旋转时，磁通匝连数按正弦规律变化：

NΦ = BAN cos(ωt)

Applying Faraday's law gives the induced EMF:

应用法拉第定律可得感应电动势：

EMF = BANω sin(ωt)

6. RMS Values of Alternating Current | 交流电的有效值

Alternating currents and voltages are usually specified by their root-mean-square (RMS) values, which are the equivalent DC values that deliver the same average power to a resistor.

交流电流和电压通常用均方根值来标定，均方根值是能够向电阻传递相同平均功率的等效直流值。

For a sinusoidal supply:

对于正弦交流电源：

Vrms = V₀/√2

Irms = I₀/√2

The average power dissipated in a resistor is given by:

电阻消耗的平均功率为：

Pavg = Vrms Irms = Irms² R

ing the angular speed doubles the peak EMF, and therefore increases the RMS output by a factor of 2.

由于发电机的V₀ = BANω，将角速度加倍可使峰值电动势加倍，从而使有效值输出增大到原来的2倍。

7. Transformers | 变压器

A transformer consists of a primary coil of Nₚ turns and a secondary coil of Nₛ turns wound on a soft iron core. An alternating voltage across the primary produces a changing flux in the core, which induces an EMF in the secondary.

变压器由匝数为Nₚ的原线圈和匝数为Nₛ的副线圈绕在软铁芯上构成。原线圈上的交变电压在铁芯中产生变化磁通，从而在副线圈中感应出电动势。

For an ideal transformer:

对于理想变压器：

Vₛ/Vₚ = Nₛ/Nₚ

Vₚ Iₚ = Vₛ Iₛ

The power equation assumes no energy losses. In real transformers, energy is lost through:

功率公式假设没有能量损失。实际变压器中的能量损失包括：