📚 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
The unit of magnetic flux is the weber (Wb), where 1 Wb = 1 T m². The flux linkage 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
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The flux is maximum when the coil plane is perpendicular to the field (θ = 0°), giving Φ = BA.
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当线圈平面垂直于磁场时（θ = 0°），磁通量最大，此时Φ = BA。
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The flux is zero when the coil plane is parallel to the field (θ = 90°).
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当线圈平面平行于磁场时（θ = 90°），磁通量为零。
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Flux density B is measured in tesla (T) and represents the flux per unit area perpendicular to the field.
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磁感应强度B的单位是特斯拉（T），表示垂直于磁场方向单位面积上的磁通量。
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：
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Determine the direction of the external magnetic field.
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判断外加磁场的方向。
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Decide whether the magnetic flux through the circuit is increasing or decreasing.
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判断穿过回路的磁通量是增大还是减小。
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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.
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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
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)
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The maximum (peak) EMF is EMF₀ = BANω, reached when the coil plane is parallel to the field.
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最大（峰值）电动势为EMF₀ = BANω，在线圈平面平行于磁场时达到。
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The EMF is zero when the coil plane is perpendicular to the field because the rate of change of flux is momentarily zero.
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当线圈平面垂直于磁场时电动势为零，因为此时磁通量的变化率瞬时为零。
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：
V_rms = V₀/√2
I_rms = I₀/√2
The average power dissipated in a resistor is given by:
电阻消耗的平均功率为：
P_avg = V_rms I_rms = I_rms² R
Since V₀ = BANω for a generator, doubling 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：
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