📚 Electromagnetic Induction for IB WJEC Physics: Key Concepts and Exam Focus | IB WJEC 物理：电磁感应 考点精讲
Electromagnetic induction is the fundamental principle behind generators, transformers, and many modern technologies. This article provides an in-depth revision of key concepts, required formulas, and typical exam questions for the IB and WJEC physics syllabuses, helping students build a solid understanding and perform well in assessments.
电磁感应是发电机、变压器和许多现代技术背后的基本原理。本文针对IB和WJEC物理课程大纲，深入复习关键概念、必备公式和典型考题，帮助学生建立扎实的理解，在考试中取得好成绩。
1. Magnetic Flux and Flux Linkage | 磁通量与磁链
Magnetic flux (Φ) is a measure of the quantity of magnetic field lines passing through a given area. For a uniform magnetic field B making an angle θ with the normal to a surface of area A, flux is defined as Φ = BA cos θ. The SI unit is the weber (Wb).
磁通量（Φ）是衡量穿过给定面积的磁场线数量的物理量。对于与面积为A的表面法线成角度θ的匀强磁场B，磁通量定义为Φ = BA cos θ。国际单位是韦伯（Wb）。
When a coil has N turns, the total flux linkage is NΦ. Flux linkage becomes central in calculating induced emf because changing the flux linkage through a coil induces an emf across its terminals.
当线圈有N匝时，总磁链为NΦ。磁链在计算感应电动势时至关重要，因为通过线圈的磁链发生变化会在线圈两端产生感应电动势。
Φ = BA 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 equal to the rate of change of magnetic flux linkage through the circuit. Mathematically, ε = −N (ΔΦ/Δt). The average emf can be found from the gradient of a flux–time graph.
法拉第定律指出，电路中感应电动势的大小等于穿过电路的磁链变化率。数学表达式为 ε = −N (ΔΦ/Δt)。平均电动势可以通过磁通量-时间图的斜率求得。
For a continuously varying flux, the instantaneous emf is given by the derivative ε = −N(dΦ/dt). The negative sign indicates the direction of the induced emf, which is described by Lenz’s law.
对于连续变化的磁通量，瞬时电动势由导数 ε = −N(dΦ/dt) 给出。负号表示感应电动势的方向，这由楞次定律描述。
3. Lenz’s Law and Direction of Induced EMF | 楞次定律与感应电动势方向
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 the conservation of energy. Without this opposition, a small change would lead to a runaway increase in current, violating energy conservation.
楞次定律指出，感应电流的方向总是使它产生的磁场阻碍引起感应电流的磁通量变化。这是能量守恒的结果。如果没有这种阻碍，微小的变化将导致电流无限增长，违背能量守恒。
In practice, to determine the direction of induced current, first identify the change in external flux (increasing or decreasing), then determine the induced magnetic field that opposes the change, and finally apply the right-hand grip rule to find current direction in the coil.
在实践中，要确定感应电流的方向，首先确定外部磁通量的变化（增大或减小），然后确定阻碍该变化的感应磁场方向，最后应用右手螺旋定则找到线圈中的电流方向。
4. Motional EMF and Conductors Moving in a Magnetic Field | 动生电动势与磁场中运动的导体
When a straight conductor of length L moves with velocity v perpendicular to a uniform magnetic field B, the charges inside experience a magnetic force. An emf is induced between the ends, given by ε = BLv, provided B, L, and v are mutually perpendicular.
当长度为L的直导体以速度v垂直于匀强磁场B运动时，导体内的电荷受到磁力作用。两端之间感应出电动势，其大小为 ε = BLv，前提是B、L和v相互垂直。
This motional emf can be derived from Faraday’s law by considering the area swept per unit time. It is the principle behind the operation of simple generators and is used in questions involving a rod on rails or a rotating coil.
这种动生电动势可以通过考虑单位时间内扫过的面积由法拉第定律推导出来。它是简单发电机的工作原理，常用在涉及导轨上的金属棒或旋转线圈的题目中。
5. AC Generator and Alternating EMF | 交流发电机与交变电动势
An AC generator consists of a coil rotating at constant angular speed ω in a uniform magnetic field. The flux linkage varies sinusoidally, and the induced emf is ε = ε₀ sin ωt, where the peak emf ε₀ = NBAω. Here N is the number of turns, A the coil area, and B the magnetic flux density.
交流发电机由在匀强磁场中以恒定角速度ω旋转的线圈构成。磁链随时间正弦变化，感应电动势为 ε = ε₀ sin ωt，峰值电动势 ε₀ = NBAω，其中N是匝数，A为线圈面积，B为磁通密度。
Exam problems often ask students to sketch the emf–time graph, calculate the rms value (ε_rms = ε₀/√2), or relate the frequency to the mechanical rotation rate. The output can be displayed on an oscilloscope to show a sine wave.
考试中经常要求学生画出电动势-时间图，计算有效值（ε_rms = ε₀/√2），或将频率与机械转速关联起来。输出信号可以在示波器上显示为正弦波。
6. Transformers: Principles and Efficiency | 变压器：原理与效率
A transformer changes the voltage of an alternating current. It consists of two coils wound on a common soft iron core. An alternating current in the primary coil creates a varying magnetic flux in the core, which links to the secondary coil, inducing an emf.
变压器改变交流电压。它由绕在共用软铁芯上的两个线圈组成。初级线圈中的交变电流在铁芯中产生变化的磁通，磁通耦合到次级线圈，从而感应出电动势。
For an ideal transformer, primary and secondary voltages are related to the turns ratio: V_s/V_p = N_s/N_p. Power is conserved, so V_p I_p = V_s I_s. Real transformers lose energy due to resistive heating, eddy currents, and hysteresis in the core.
对于理想变压器，初级与次级电压的关系由匝数比决定：V_s/V_p = N_s/N_p。功率守恒，因此 V_p I_p = V_s I_s。实际变压器由于电阻发热、涡流和铁芯磁滞而损失能量。
V_s/V_p = N_s/N_p | Efficiency = (V_s I_s)/(V_p I_p) × 100%
7. Eddy Currents and Their Applications | 涡流及其应用
Eddy currents are circulating currents induced in a solid conductor when it experiences a changing magnetic field. According to Lenz’s law, they flow in closed loops within the metal and generate their own magnetic field opposing the change, producing a braking effect.
涡流是块状导体处于变化的磁场中时，其内部感应出的环行电流。根据楞次定律，它们在金属内部形成闭合回路，产生阻碍变化的磁场，从而产生制动效果。
Eddy currents are exploited in electromagnetic braking in trains, induction hobs, and metal detectors. In transformers, they are undesirable because they cause energy loss, so the core is laminated to restrict their paths.
涡流被用于火车电磁制动、电磁炉和金属探测器中。在变压器中，它们引起能量损失是不希望出现的，因此铁芯采用叠片结构来限制涡流路径。
8. Self-Inductance and Mutual Inductance | 自感与互感
Self-inductance (L) is the property of a coil by which a change in current induces an opposing emf within the same coil. The induced back emf is ε = −L (dI/dt). The unit of inductance is the henry (H).
自感（L）是线圈由于自身电流变化而在同一线圈内感应出反向电动势的性质。感应出的反向电动势为 ε = −L (dI/dt)。电感的单位是亨利（H）。
Mutual inductance (M) describes how a changing current in one coil induces an emf in a neighbouring coil. It underlies transformer operation, where ε_s = −M (dI_p/dt). The value of M depends on the geometry and the presence of a core.
互感（M）描述一个线圈中变化的电流如何在相邻线圈中感应出电动势。它是变压器工作的基础，其中 ε_s = −M (dI_p/dt)。M的值取决于几何结构和有无铁芯。
9. Energy Stored in an Inductor | 电感储能
An inductor stores energy in the magnetic field created by the current flowing through it. The energy stored is given by E = ½ L I². This is analogous to a capacitor storing energy in an electric field.
电感器将能量储存在由通过其电流产生的磁场中。储存的能量为 E = ½ L I²。这与电容器在电场中储存能量类似。
In circuits, when the current through an inductor is interrupted, the collapsing magnetic field can induce a large emf, potentially causing sparks or damage. Flyback diodes are used to protect components.
在电路中，当通过电感的电流被切断时，坍塌的磁场会感应出很大的电动势，可能引起火花或损坏元件。使用续流二极管来保护器件。
10. RL Circuits and Time Constants | RL电路与时间常数
An RL circuit consists of a resistor and an inductor in series. When connected to a DC source, the current does not rise instantly but grows exponentially: I = I₀ (1 − e^(−t/τ)), where τ = L/R is the time constant. After one time constant, current reaches about 63% of its final value.
RL电路由电阻与电感串联组成。当接到直流电源时，电流不会立即达到最大值，而是按指数规律增长：I = I₀ (1 − e^(−t/τ))，其中τ = L/R为时间常数。经过一个时间常数后，电流约达最终值的63%。
When the source is removed, the current decays exponentially: I = I₀ e^(−t/τ). The time constant governs the rate of energy storage and release in practical applications such as electromagnets and motor windings.
移除电源后，电流按指数衰减：I = I₀ e^(−t/τ)。时间常数决定了实际应用中电磁铁和电机绕组储能与释放能量的速率。
11. Common Experimental Investigations | 常见实验探究
Key experiments include dropping a magnet through a coil connected to a data logger, demonstrating Faraday’s law and Lenz’s law by observing the induced voltage peaks. The area under the voltage–time graph relates to the total flux change.
关键实验包括将磁铁穿过连接到数据采集器的线圈，观察感应电压峰来验证法拉第定律和楞次定律。电压-时间图下的面积与总磁通变化相关。
Another classic setup is the ‘jumping ring’ demonstration, where a conducting ring jumps off an iron core when an AC current is turned on, vividly illustrating repulsion due to induced eddy currents.
另一个经典装置是“跳环”演示，当接通交流电时，导电环从铁芯上跳起，生动展示了感应涡流产生的排斥力。
12. Exam Tips and Common Pitfalls | 考试技巧与常见误区
Always pay attention to the negative sign in ε = −N (ΔΦ/Δt); it indicates direction, not magnitude. When calculating motional emf, check that B, L, and v are truly perpendicular; otherwise use appropriate components.
始终注意 ε = −N (ΔΦ/Δt) 中的负号；它表示方向，不是大小。计算动生电动势时，确认B、L和v确实相互垂直；否则使用合适的分量。
Confusing flux (Φ) and flux linkage (NΦ) is a common mistake. Also, remember that the induced emf depends on the rate of change of flux, not the flux itself. A constant flux produces zero emf even if the flux is large.
混淆磁通量（Φ）和磁链（NΦ）是常见错误。还要记住，感应电动势取决于磁通量的变化率，而不是磁通量本身。即使磁通量很大，恒定的磁通也不会产生电动势。
In transformer calculations, assume ideal conditions unless stated otherwise, but be ready to discuss efficiency and energy losses. Clearly state the steps when applying Lenz’s law to determine current direction.
在变压器计算中，除非另有说明，默认理想条件，但要做好讨论效率和能量损失的准备。应用楞次定律确定电流方向时，清晰列出步骤。
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