A-Level WJEC Science: Electricity and Magnetism – Key Points Review | A-Level WJEC 科学：电与磁考点精讲

📚 A-Level WJEC Science: Electricity and Magnetism – Key Points Review | A-Level WJEC 科学：电与磁考点精讲

Electricity and magnetism form the backbone of classical physics, and the WJEC A-Level Science specification demands a firm grasp of both qualitative concepts and quantitative problem-solving. This revision guide breaks down the essential topics, equations, and practical applications you must master. From Coulomb’s law to Faraday’s induction, every key point is explained with clarity and paired with its Chinese equivalent to support bilingual learning.

电与磁构成了经典物理学的支柱，WJEC A-Level 科学大纲要求对定性概念和定量解题都要有牢固的掌握。这份复习指南分解了你必须掌握的核心主题、方程式和实际应用。从库仑定律到法拉第感应，每个考点都以清晰的方式解释，并配有中文翻译，以支持双语学习。

1. Electric Fields and Coulomb’s Law | 电场与库仑定律

An electric field is a region where a charged particle experiences a force. The field strength E is defined as the force per unit positive charge.

电场是带电粒子会受到力的区域。电场强度 E 定义为单位正电荷所受的力。

Coulomb’s law states that the force F between two point charges Q₁ and Q₂ separated by distance r is: F = k|Q₁Q₂| / r², where k = 1/(4πε₀).

库仑定律指出，两个点电荷 Q₁ 和 Q₂ 之间相距 r 时的作用力 F 为：F = k|Q₁Q₂| / r²，其中 k = 1/(4πε₀)。

For opposite charges, the force is attractive; for like charges, it is repulsive.

异种电荷相互吸引；同种电荷相互排斥。
Electric field strength for a point charge is E = kQ/r² and it is a vector quantity directed radially outward from a positive charge.

点电荷的电场强度为 E = kQ/r²，它是矢量，方向从正电荷径向向外。
Uniform electric fields, as between parallel plates, have constant magnitude E = V/d, where V is the potential difference and d is plate separation.

平行板之间的匀强电场具有恒定大小 E = V/d，其中 V 是电势差，d 是板间距。

2. Electric Potential and Energy | 电势与电势能

Electric potential V at a point is the work done per unit charge in bringing a positive test charge from infinity to that point. It is a scalar quantity measured in volts (J/C).

电势 V 是单位正电荷从无限远处移动到该点所做的功。它是标量，单位为伏特 (J/C)。

For a point charge Q, V = kQ/r. The potential energy of two charges Q₁ and Q₂ separated by r is U = kQ₁Q₂/r.

对于点电荷 Q，V = kQ/r。两个电荷 Q₁ 和 Q₂ 相距 r 时的电势能为 U = kQ₁Q₂/r。

The potential difference between two points A and B is V_AB = V_A – V_B, and work done W = qΔV.

两点 A、B 之间的电势差为 V_AB = V_A – V_B，做功 W = qΔV。
Equipotential surfaces are perpendicular to field lines, and no work is done moving a charge along an equipotential.

等势面与电场线垂直，沿等势面移动电荷不做功。

3. Capacitance and Capacitors | 电容与电容器

Capacitance C is the charge stored per unit potential difference: C = Q/V. The unit is the farad (F). A capacitor stores energy in the electric field between its plates.

电容 C 是单位电势差下储存的电荷量：C = Q/V，单位是法拉 (F)。电容器将能量储存在两极板间的电场中。

For a parallel-plate capacitor, C = ε₀A/d, where A is plate area and d is separation. Adding a dielectric increases capacitance by a factor εᵣ (relative permittivity).

对于平行板电容器，C = ε₀A/d，其中 A 是极板面积，d 是间距。加入电介质使电容增大 εᵣ（相对介电常数）倍。

Energy stored = ½QV = ½CV² = ½Q²/C. The charging and discharging of a capacitor through a resistor follow exponential laws with time constant τ = RC.

储存能量 = ½QV = ½CV² = ½Q²/C。电容器通过电阻充放电遵循指数规律，时间常数 τ = RC。

4. Current, Resistance, and Ohm’s Law | 电流、电阻与欧姆定律

Electric current I is the rate of flow of charge: I = ΔQ/Δt. In metals, current is carried by free electrons. Conventional current direction is opposite to electron flow.

电流 I 是电荷流动的速率：I = ΔQ/Δt。在金属中，电流由自由电子承载。常规电流方向与电子流动方向相反。

Ohm’s law states that V = IR for ohmic conductors at constant temperature. Resistance R depends on resistivity ρ, length L, and cross-sectional area A: R = ρL/A.

欧姆定律指出，对于恒温下的欧姆导体，V = IR。电阻 R 取决于电阻率 ρ、长度 L 和横截面积 A：R = ρL/A。

Resistance increases with temperature in metals due to increased lattice vibrations; semiconductors typically show a decrease.

金属电阻随温度升高而增大，因为晶格振动加剧；半导体通常电阻随温度升高而减小。
Power dissipated: P = IV = I²R = V²/R.

功率耗散：P = IV = I²R = V²/R。

5. DC Circuits and Kirchhoff’s Laws | 直流电路与基尔霍夫定律

Kirchhoff’s current law (KCL): the sum of currents entering a junction equals the sum leaving. Kirchhoff’s voltage law (KVL): the sum of e.m.f.s around a closed loop equals the sum of p.d.s.

基尔霍夫电流定律 (KCL)：流入节点的电流之和等于流出之和。基尔霍夫电压定律 (KVL)：沿闭合回路的电动势之和等于电势差之和。

Series circuits: current is the same through all components; total resistance R_total = R₁ + R₂ + … . Parallel circuits: voltage is the same across each branch; 1/R_total = 1/R₁ + 1/R₂ + … .

串联电路：通过所有元件的电流相同；总电阻 R_total = R₁ + R₂ + … 。并联电路：各支路电压相同；1/R_total = 1/R₁ + 1/R₂ + … 。

Internal resistance r of a cell causes terminal p.d. V = ε − Ir, where ε is the e.m.f.

电池的内阻 r 导致端电压 V = ε − Ir，其中 ε 为电动势。

6. Magnetic Fields and Forces on Moving Charges | 磁场与运动电荷受力

A magnetic field exerts a force on a moving charged particle. The force F = qvB sinθ, where q is the charge, v its velocity, B the magnetic flux density, and θ the angle between v and B.

磁场对运动带电粒子施加力。力 F = qvB sinθ，其中 q 是电荷，v 是速度，B 是磁通量密度，θ 是 v 与 B 的夹角。

The direction of force is given by Fleming’s left-hand rule (for positive charge) or the right-hand slap rule: thumb – force, first finger – field, second finger – velocity. For a negative charge, reverse the force direction.

力的方向由弗莱明左手定则确定（正电荷）：拇指 – 力，食指 – 磁场，中指 – 速度。对于负电荷，力反向。

In a uniform magnetic field, a charged particle moving perpendicular to the field follows a circular path with radius r = mv/(qB).

在匀强磁场中，垂直于磁场运动的带电粒子轨迹为圆，半径 r = mv/(qB)。
The cyclotron frequency f = qB/(2πm) is independent of speed.

回旋频率 f = qB/(2πm) 与速度无关。

7. Magnetic Flux and Flux Linkage | 磁通量与磁链

Magnetic flux Φ is the product of the magnetic flux density B and the area A perpendicular to the field: Φ = BA cosθ. The unit is the weber (Wb).

磁通量 Φ 是磁通量密度 B 与垂直于磁场的面积 A 的乘积：Φ = BA cosθ，单位为韦伯 (Wb)。

Flux linkage NΦ is the product of the number of turns N on a coil and the flux through each turn. It is crucial in calculating induced e.m.f.

磁链 NΦ 是线圈匝数 N 与每匝磁通量的乘积，对计算感应电动势至关重要。

8. Electromagnetic Induction and Faraday’s Law | 电磁感应与法拉第定律

Faraday’s law: the magnitude of induced e.m.f. is equal to the rate of change of flux linkage: ε = −N ΔΦ/Δt. The negative sign indicates Lenz’s law.

法拉第定律：感应电动势的大小等于磁链变化率：ε = −N ΔΦ/Δt。负号表示楞次定律。

Lenz’s law states that the direction of induced current is such that it opposes the change in magnetic flux that produced it. This is a consequence of energy conservation.

楞次定律指出，感应电流的方向总是反抗引起它的磁通量变化，这是能量守恒的结果。

An e.m.f. is induced when there is relative motion between a conductor and a magnetic field, or when the field through a coil changes.

当导体与磁场之间存在相对运动，或通过线圈的磁场变化时，就会产生感应电动势。

9. The Motor Effect and Force on a Current-Carrying Conductor | 电动机效应与通电导体受力

A current-carrying conductor in a magnetic field experiences a force: F = BIL sinθ, where I is current, L is length of conductor in the field, and θ is the angle between the current and B.

磁场中的通电导体受到作用力：F = BIL sinθ，其中 I 为电流，L 为导体在磁场中的长度，θ 为电流与 B 的夹角。

Use Fleming’s left-hand rule for direction: thumb – force (motion), first finger – field (N to S), second finger – current (conventional).

方向使用弗莱明左手定则：拇指 – 力（运动），食指 – 磁场（N 到 S），中指 – 电流（常规方向）。

This effect is the principle behind electric motors, where a coil rotates in a magnetic field due to the torque τ = BANI sinθ (A = coil area, N = turns).

这是电动机的原理，线圈在磁场中因力矩 τ = BANI sinθ（A = 线圈面积，N = 匝数）而旋转。

10. Alternating Current and Transformers | 交流电与变压器

Alternating current (AC) periodically reverses direction. The root-mean-square (rms) value of an AC is I_rms = I₀/√2, V_rms = V₀/√2, where I₀ and V₀ are peak values.

交流电 (AC) 周期性改变方向。有效值 (rms) 为 I_rms = I₀/√2，V_rms = V₀/√2，其中 I₀ 和 V₀ 为峰值。

A transformer consists of primary and secondary coils wound on a laminated iron core. It transfers electrical energy via changing magnetic flux. For an ideal transformer, V_s / V_p = N_s / N_p and P_p = P_s.

变压器由绕在叠片铁芯上的初级和次级线圈构成，通过变化的磁通传递电能。对于理想变压器，V_s / V_p = N_s / N_p 且 P_p = P_s。

Step-up: N_s > N_p, voltage increased; step-down: N_s < N_p, voltage decreased.

升压：N_s > N_p，电压升高；降压：N_s < N_p，电压降低。
Eddy currents in the core are reduced by lamination, improving efficiency.

铁芯中的涡流通过叠片结构减小，提高效率。

11. Lenz’s Law and Induction Applications | 楞次定律与感应应用

Lenz’s law explains back e.m.f. in motors and the damping effect in electromagnetic braking. The induced current creates a field that opposes the motion of a magnet towards or away from a coil.

楞次定律解释了电动机中的反电动势以及电磁制动中的阻尼效应。感应电流产生的磁场反抗磁铁靠近或远离线圈的运动。

Eddy currents circulating in a conductor experience a force that opposes motion, used in non-contact braking systems.

在导体中循环的涡流受到反抗运动的力，用于非接触制动系统。

Applications include generators, where mechanical energy is converted to electrical energy by rotating a coil in a magnetic field, and induction cooktops, where a changing magnetic field induces eddy currents in the pan base to generate heat.

应用包括将机械能转化为电能的发电机（通过线圈在磁场中旋转），以及电磁炉（变化的磁场在锅底感应出涡流产生热量）。

12. Practical Circuit Analysis and Measurement | 电路分析与测量实践

When measuring current and voltage, ammeters are connected in series (low internal resistance) and voltmeters in parallel (high internal resistance). Multimeters can measure AC/DC quantities.

测量电流和电压时，安培表串联（低内阻），伏特表并联（高内阻）。万用表可测量交直流量。

Potential divider circuits provide variable voltage output: V_out = V_in × (R₂/(R₁+R₂)). They are widely used in sensor circuits with LDRs and thermistors.

分压电路提供可变电压输出：V_out = V_in × (R₂/(R₁+R₂))，广泛用于含光敏电阻和热敏电阻的传感器电路。

Component	Behavior
LDR (Light Dependent Resistor)	Resistance decreases with increasing light intensity
热敏电阻 LDR（光敏电阻）	电阻随光照强度增加而减小
Thermistor (NTC type)	Resistance decreases as temperature rises
热敏电阻（NTC型）	电阻随温度升高而减小

WJEC practicals often include investigating capacitor charging/discharging curves and verifying Faraday’s law. Ensure you can plot and interpret ln(V) vs time graphs to determine RC time constant.

WJEC 实验通常包括研究电容器充放电曲线和验证法拉第定律。确保你能绘制并解读 ln(V)-时间图以确定 RC 时间常数。

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A-Level WJEC Science: Electricity and Magnetism – Key Points Review | A-Level WJEC 科学：电与磁 考点精讲