📚 IB AQA Science: Electricity and Magnetism Exam Guide | IB AQA 科学：电与磁考点精讲
Electricity and magnetism lie at the heart of modern physics, bridging concepts from atomic charge to large‑scale power generation. Whether you are studying under the IB diploma or AQA specification, mastering these topics is essential for problem solving and understanding how the physical world operates. This revision guide breaks down the most tested concepts into clear, bilingual explanations to boost your confidence in the exam hall.
电与磁是现代物理的核心，从原子电荷到大规模发电，二者紧密相连。无论你是在学习 IB 文凭课程还是 AQA 考纲，掌握这些主题对解题和理解物理世界至关重要。这份考点指南将最常考的概念分解为中英双语清晰讲解，助你在考场上信心倍增。
1. Electric Charge and Current | 电荷与电流
Charge (Q) is a fundamental property of matter. Protons carry positive charge and electrons carry negative charge. The unit is the coulomb (C), and the elementary charge e = 1.60 × 10⁻¹⁹ C. An object becomes charged by gaining or losing electrons. Charge is quantised: Q = n e, where n is an integer.
电荷 (Q) 是物质的基本属性。质子带正电荷，电子带负电荷。单位是库仑 (C)，基本电荷 e = 1.60 × 10⁻¹⁹ C。物体通过得失电子而带电。电荷是量子化的：Q = n e，其中 n 为整数。
Electric current (I) is the rate of flow of charge. In a metal, it is the drift of free electrons. Direct current (d.c.) flows in one direction, while alternating current (a.c.) periodically reverses. Current is measured in amperes (A), and 1 A = 1 C s⁻¹.
电流 (I) 是电荷的流动速率。在金属中，电流来自自由电子的漂移。直流电 (d.c.) 单向流动，而交流电 (a.c.) 周期性改变方向。电流以安培 (A) 为单位，1 A = 1 C s⁻¹。
The conventional current direction is taken as the flow of positive charge, opposite to electron movement. The equation I = nAvq describes current in a conductor with charge carrier density n, cross‑sectional area A, drift velocity v and carrier charge q.
惯例电流方向取正电荷流动方向，与电子运动方向相反。方程 I = nAvq 描述了导体内电流，其中 n 为载流子密度，A 为截面积，v 为漂移速度，q 为载流子电荷。
2. Potential Difference and EMF | 电势差与电动势
Potential difference (p.d.) between two points is the work done per unit charge to move charge between them. The unit is the volt (V); 1 V = 1 J C⁻¹. P.d. is often called voltage and is measured with a voltmeter connected in parallel.
两点之间的电势差 (p.d.) 是将单位电荷从一点移动到另一点所做的功。单位是伏特 (V)；1 V = 1 J C⁻¹。电势差常被称作电压，需将电压表并联测量。
Electromotive force (e.m.f.) is the total energy supplied per unit charge by a source such as a battery. It is measured in volts. In an open circuit, the terminal p.d. equals the e.m.f.; when current flows, the terminal p.d. drops due to internal resistance r.
电动势 (e.m.f.) 是电源（如电池）每单位电荷提供的总能量，单位为伏特。在开路中，路端电压等于电动势；有电流时，因内阻 r 路端电压会下降。
The relationship is: V = ε – I r, where ε is e.m.f., V is terminal p.d., I is current and r is internal resistance. Internal resistance can be found from the gradient of a V–I graph.
关系式为：V = ε – I r，其中 ε 为电动势，V 为路端电压，I 为电流，r 为内阻。内阻可通过 V–I 图线的斜率求得。
3. Resistance and Ohm’s Law | 电阻与欧姆定律
Resistance (R) measures how much a component opposes current. The unit is the ohm (Ω). Ohm’s law states that for a metallic conductor at constant temperature, the current is directly proportional to the potential difference: V = I R.
电阻 (R) 衡量元件对电流的阻碍程度，单位是欧姆 (Ω)。欧姆定律指出，对温度不变的金属导体，电流与电势差成正比：V = I R。
Resistance depends on the material and dimensions: R = ρ L / A, where ρ is resistivity (Ω m), L is length and A is cross‑sectional area. Resistivity depends on temperature and material type. A filament lamp exhibits non‑ohmic behaviour because its temperature rises with current, increasing resistance.
电阻取决于材料与尺寸：R = ρ L / A，其中 ρ 为电阻率 (Ω m)，L 为长度，A 为横截面积。电阻率取决于温度和材料种类。灯丝灯泡表现出非欧姆特性，因为电流增大导致温度升高，电阻随之增加。
A semiconductor thermistor and a light‑dependent resistor (LDR) also show non‑linear I–V characteristics. The I–V graph for a diode shows that current passes easily in one direction but is almost zero in the reverse direction.
半导体热敏电阻和光敏电阻 (LDR) 也表现出非线性 I–V 特性。二极管的 I–V 图显示在一个方向上电流容易通过，反向时电流几乎为零。
4. Series and Parallel Circuits | 串联与并联电路
In a series circuit, the current is the same at all points: I = I₁ = I₂. The total resistance is the sum of individual resistances: Rₜₒₜₐₗ = R₁ + R₂ + … . The supply voltage is shared: V = V₁ + V₂.
在串联电路中，各点电流相等：I = I₁ = I₂。总电阻等于各电阻之和：Rₜₒₜₐₗ = R₁ + R₂ + … 。电源电压被分配：V = V₁ + V₂。
In a parallel circuit, the p.d. across each branch is the same: V = V₁ = V₂. The total current is the sum of branch currents: I = I₁ + I₂. The reciprocal formula for total resistance is 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂.
在并联电路中，各支路两端的电势差相同：V = V₁ = V₂。总电流等于各支路电流之和：I = I₁ + I₂。总电阻的倒数公式为 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂。
Combination circuits require step‑by‑step simplification. Additionally, power (P) dissipated in a resistor can be expressed as P = I V = I² R = V² / R. This is useful for comparing the brightness of bulbs or heating effects.
混联电路需要逐步化简。此外，电阻器消耗的功率 (P) 可表示为 P = I V = I² R = V² / R。这适用于比较灯泡亮度或热效应。
5. Kirchhoff’s Laws and Circuit Analysis | 基尔霍夫定律与电路分析
Kirchhoff’s first law (the junction rule) states that the algebraic sum of currents entering a junction equals the sum of currents leaving it. This is a consequence of charge conservation: Σ Iᵢₙ = Σ Iₒᵤₜ.
基尔霍夫第一定律（节点定律）指出，流入节点的电流代数和等于流出节点的电流代数和。这是电荷守恒的结果：Σ Iᵢₙ = Σ Iₒᵤₜ。
Kirchhoff’s second law (the loop rule) states that the sum of e.m.f.s around any closed loop equals the sum of p.d.s in that loop: Σ ε = Σ I R. This follows from energy conservation. These laws are essential for analysing complex circuits with multiple loops and power supplies.
基尔霍夫第二定律（回路定律）指出，沿任一闭合回路的电动势之和等于该回路中电势降之和：Σ ε = Σ I R。这源于能量守恒。这两条定律对分析含多个回路和电源的复杂电路至关重要。
Potential dividers are a common application. A simple divider of two resistors in series yields Vₒᵤₜ = Vᵢₙ × (R₂ / (R₁ + R₂)). Potentiometers, thermistors and LDRs in divider circuits provide variable voltage outputs for sensor applications.
分压器是一种常见应用。两个电阻串联构成的简单分压器输出 Vₒᵤₜ = Vᵢₙ × (R₂ / (R₁ + R₂))。电位器、热敏电阻和光敏电阻在分压电路中用于传感器，提供可变电压输出。
6. Capacitance and Energy Storage | 电容与能量储存
A capacitor stores charge and energy in an electric field between two conducting plates separated by an insulator. Capacitance C is defined as C = Q / V, measured in farads (F). For a parallel‑plate capacitor, C = ε₀ εᵣ A / d, where ε₀ is the permittivity of free space, εᵣ the relative permittivity, A the plate area and d the separation.
电容器通过两块被绝缘体隔开的导体板之间的电场储存电荷和能量。电容 C 定义为 C = Q / V，单位法拉 (F)。对平行板电容器，C = ε₀ εᵣ A / d，其中 ε₀ 为真空介电常数，εᵣ 为相对介电常数，A 为极板面积，d 为间距。
The energy stored in a capacitor is E = ½ Q V = ½ C V² = ½ Q² / C. In an RC circuit, charging and discharging follow exponential curves: Q = Q₀ (1 – e^{-t/RC}) for charging, and Q = Q₀ e^{-t/RC} for discharging. The time constant τ = R C determines how quickly the capacitor charges or discharges.
电容器储存的能量为 E = ½ Q V = ½ C V² = ½ Q² / C。在 RC 电路中，充电和放电遵循指数曲线：充电时 Q = Q₀ (1 – e^{-t/RC})，放电时 Q = Q₀ e^{-t/RC}。时间常数 τ = R C 决定电容器充放电的快慢。
Examiners often ask for graphical interpretation of discharge curves or half‑life calculations. The half‑life t₁/₂ = R C ln 2 is a key relationship for data analysis.
考官常要求解释放电曲线图或进行半衰期计算。半衰期 t₁/₂ = R C ln 2 是数据分析中的关键关系式。
7. Magnetic Fields and Forces on Charges | 磁场与电荷受力
A magnetic field is a region where moving charges experience a force. It is represented by field lines that run from north to south. The magnetic flux density B, measured in teslas (T), indicates the strength of the field. The force on a current‑carrying wire in a uniform field is F = B I L sinθ, where θ is the angle between the wire and the field.
磁场是运动电荷受力的区域，用从北指向南的磁感线表示。磁通量密度 B，单位特斯拉 (T)，表示磁场强度。载流导线在匀强磁场中受力为 F = B I L sinθ，其中 θ 为导线与磁场的夹角。
For a single moving charge, the force (Lorentz force) is F = q v B sinθ. The direction of force is given by Fleming’s left‑hand rule (for current in a wire) or the right‑hand palm rule for positive charges. The force is always perpendicular to both velocity and field, resulting in circular motion for a charge entering a uniform field perpendicularly.
对于单个运动电荷，洛伦兹力为 F = q v B sinθ。力的方向由左手定则（导线电流）或正电荷右手掌定则判定。力总是垂直于速度和磁场，导致电荷垂直进入匀强磁场时做圆周运动。
The radius of the circular path is r = m v / (q B). Applications include mass spectrometers, velocity selectors and cyclotrons. In a velocity selector, electric and magnetic forces balance: q E = q v B, so v = E / B.
圆周路径半径 r = m v / (q B)。应用包括质谱仪、速度选择器和回旋加速器。在速度选择器中，电场力与磁力平衡：q E = q v B，因此 v = E / B。
8. Electromagnetic Induction and Lenz’s Law | 电磁感应与楞次定律
Electromagnetic induction occurs when there is a change in magnetic flux Φ through a coil. Magnetic flux Φ = B A cosθ, measured in webers (Wb). Faraday’s law states that the induced e.m.f. is proportional to the rate of change of flux linkage: ε = -N ΔΦ / Δt, where N is the number of turns.
当通过线圈的磁通量 Φ 发生变化时，就会发生电磁感应。磁通量 Φ = B A cosθ，单位韦伯 (Wb)。法拉第定律指出，感应电动势与磁链变化率成正比：ε = -N ΔΦ / Δt，N 为匝数。
Lenz’s law gives the direction of the induced e.m.f.: the induced current flows so as to oppose the change in flux that produced it. This explains the negative sign in Faraday’s law. It is a consequence of energy conservation.
楞次定律给出了感应电动势的方向：感应电流的方向总是试图阻碍引起它的磁通量变化。这解释了法拉第定律中的负号，也是能量守恒的体现。
Generators and dynamos convert mechanical energy into electrical energy using induction. A coil rotating in a uniform magnetic field generates a sinusoidal e.m.f. The peak e.m.f. is ε₀ = N B A ω, where ω is the angular speed. Alternators produce a.c., and with a split‑ring commutator a d.c. dynamo can be made.
发电机利用感应将机械能转化为电能。线圈在匀强磁场中旋转产生正弦交流电动势。峰值电动势 ε₀ = N B A ω，ω 为角速度。交流发电机产生交流电，使用裂环换向器则可制成直流发电机。
9. AC Circuits and Transformers | 交流电路与变压器
Alternating current (a.c.) varies sinusoidally: I = I₀ sin(ω t), V = V₀ sin(ω t). The root mean square (r.m.s.) values are useful for power calculations: Iᵣₘₛ = I₀ / √2, Vᵣₘₛ = V₀ / √2. Average power in a resistive circuit is P = Iᵣₘₛ Vᵣₘₛ.
交流电 (a.c.) 按正弦规律变化：I = I₀ sin(ω t)，V = V₀ sin(ω t)。方均根值 (r.m.s.) 对功率计算很有用：Iᵣₘₛ = I₀ / √2，Vᵣₘₛ = V₀ / √2。纯电阻电路的平均功率 P = Iᵣₘₛ Vᵣₘₛ。
A transformer relies on mutual induction to step a.c. voltage up or down. It consists of two coils wound on a common iron core. For an ideal transformer, the power in equals power out, so Vₚ Iₚ = Vₛ Iₛ. The voltage ratio equals the turns ratio: Vₛ / Vₚ = Nₛ / Nₚ.
变压器依靠互感来实现升压或降压，由绕在共用铁芯上的两个线圈构成。理想变压器输入功率等于输出功率，故 Vₚ Iₚ = Vₛ Iₛ。电压比等于匝数比：Vₛ / Vₚ = Nₛ / Nₚ。
Real transformers have energy losses due to resistive heating, eddy currents and hysteresis. Laminated cores reduce eddy currents. Transformer efficiency is high, often above 99% for large units. Step‑up transformers are used in power transmission to reduce current and minimise I²R losses.
实际变压器因电阻发热、涡流和磁滞产生能量损耗。采用叠片铁芯可减少涡流。变压器效率很高，大型变压器常超过 99%。升压变压器用于电力传输，以降低电流并减小 I²R 损耗。
10. Electromagnetic Waves and Applications | 电磁波及其应用
Maxwell’s equations predict that a changing electric field produces a magnetic field and vice versa, giving rise to self‑propagating electromagnetic waves. These waves travel at the speed of light c = 3.00 × 10⁸ m s⁻¹ in a vacuum and require no medium. The wave equation is c = f λ.
麦克斯韦方程组预言，变化的电场产生磁场，变化的磁场产生电场，从而形成自传播的电磁波。电磁波在真空中以光速 c = 3.00 × 10⁸ m s⁻¹ 传播，无需介质。波动方程为 c = f λ。
The electromagnetic spectrum, in order of increasing frequency and energy, includes radio waves, microwaves, infrared, visible light, ultraviolet, X‑rays and gamma rays. All are transverse waves capable of reflection, refraction, diffraction and interference.
电磁波谱按频率和能量递增顺序包括：无线电波、微波、红外线、可见光、紫外线、X 射线和伽马射线。它们都是横波，能发生反射、折射、衍射和干涉。
Practical applications are huge: radio waves for communication, microwaves for cooking and radar, infrared for thermal imaging, visible light for vision, ultraviolet for sterilisation, X‑rays for medical imaging, and gamma rays for cancer treatment. In exams, you should link wave properties such as penetration or heating to the photon energy E = h f.
实际应用非常广泛：无线电波用于通信，微波用于烹饪和雷达，红外线用于热成像，可见光用于视觉，紫外线用于杀菌，X 射线用于医学成像，伽马射线用于癌症治疗。考试中，你需要将波的穿透或加热等特性与光子能量 E = h f 联系起来。
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