📚 A-Level Physics: Electricity and Magnetism Key Revision Points | A-Level 物理：电与磁考点精讲
This article distils the most important electricity and magnetism concepts required for A-Level Physics examinations. From fundamental definitions of charge and current to electromagnetic induction and transformers, each topic is presented with clear explanations and exam-relevant formulas. Understanding these core principles will not only help you solve standard problems but also tackle synoptic questions that link circuits, fields and energy conservation.
本文浓缩了A-Level物理考试中电与磁最重要的概念。从电荷与电流的基本定义，到电磁感应与变压器，每个主题都配有清晰的解释和与考试密切相关的公式。理解这些核心原理不仅能帮你解决常规问题，还能应对联系电路、场与能量守恒的综合题型。
1. Electric Charge, Current and Potential Difference | 电荷、电流与电势差
Electric charge (Q) is a fundamental property of matter, measured in coulombs (C). Current (I) is the rate of flow of charge, defined as I = ΔQ / Δt. The ampere is the base SI unit for current, and one coulomb is the charge transported by a current of one ampere in one second. In metallic conductors, this flow consists of delocalised electrons moving in the opposite direction to conventional current.
电荷(Q)是物质的基本属性，单位为库仑(C)。电流(I)是电荷的流动速率，定义为 I = ΔQ / Δt。安培是国际单位制中电流的基本单位，1库仑等于1安培电流在1秒内输送的电荷量。在金属导体中，电荷流动由自由电子组成，其运动方向与约定电流方向相反。
Potential difference (V) between two points is the work done per unit charge to move a charge between those points, stated as V = W / Q. The electromotive force (e.m.f.) of a source is the energy supplied per unit charge around a complete circuit. While both are measured in volts, e.m.f. refers to the energy conversion from chemical, mechanical or other forms into electrical energy, whereas potential difference measures the energy transferred by the charges in an external component.
两点间的电势差(V)是将单位电荷从一点移动到另一点所做的功，即 V = W / Q。电源的电动势(e.m.f.)是单位电荷绕完整电路一周所获得的能量。虽然两者都以伏特为单位，但电动势指化学能、机械能等形式转化为电能，而电势差衡量的是电荷在外电路元件上转移的能量。
2. Resistance and Ohm’s Law | 电阻与欧姆定律
Resistance (R) is the opposition to current flow, defined by R = V / I, with the unit ohm (Ω). Ohm’s law states that for a metallic conductor at constant temperature, the current through it is directly proportional to the potential difference across it, so V = I R holds as a constant ratio. The I–V characteristic of an ohmic conductor is a straight line passing through the origin.
电阻(R)是对电流的阻碍作用，由 R = V / I 定义，单位是欧姆(Ω)。欧姆定律指出，在温度不变的条件下，通过金属导体的电流与其两端的电势差成正比，因此 V = I R 保持恒定比值。欧姆导体的 I–V 特性曲线是一条过原点的直线。
Non-ohmic components, such as filament lamps and diodes, do not obey Ohm’s law. In a filament lamp, the increasing current raises the temperature, causing the resistance to increase because the metal ions vibrate more, scattering the electrons more frequently. A diode allows current to flow easily in one direction but offers extremely high resistance in the reverse direction, resulting in a threshold voltage before significant conduction occurs.
非欧姆元件，如灯丝灯泡和二极管，不遵循欧姆定律。在灯丝灯泡中，电流增大使温度升高，电阻随之增加，因为金属离子振动加剧，更频繁地散射电子。二极管允许电流沿一个方向轻松通过，但在反向偏置时呈现极高电阻，需达到阈值电压后才有明显导通。
3. Resistivity | 电阻率
Resistivity (ρ) is an intrinsic property of a material that quantifies how strongly it resists current. The resistance of a uniform wire is given by R = ρL / A, where L is the length and A is the cross-sectional area. The unit of resistivity is ohm-metre (Ω m). Good conductors, like copper, have very low resistivity, while insulators have extremely high resistivity values.
电阻率(ρ)是材料固有的属性，用来量化其阻碍电流的强度。均匀导线的电阻由公式 R = ρL / A 给出，其中 L 是长度，A 是横截面积。电阻率的单位是欧姆·米(Ω m)。良导体如铜的电阻率极低，而绝缘体的电阻率非常高。
The resistivity of a metal increases with temperature, whereas the resistivity of a semiconductor typically decreases with temperature because more charge carriers are liberated. A-level experiments often involve measuring the resistance of a wire while varying its length and plotting R against L to determine ρ from the gradient, provided the cross-sectional area is known.
金属的电阻率随温度升高而增大，而半导体因释放出更多载流子，电阻率通常随温度升高而减小。A-level实验中常通过改变导线长度测量电阻，绘制 R-L 图像，在已知横截面积的条件下由斜率求出 ρ。
4. Series and Parallel Circuits | 串联与并联电路
Understanding how current, voltage and resistance combine in different circuit arrangements is crucial for circuit analysis. The table below summarises the key rules for series and parallel connections.
理解电流、电压和电阻在不同电路连接中的组合方式是电路分析的关键。下表总结了串联和并联电路的主要规则。
| Quantity | Series connection / 串联 | Parallel connection / 并联 |
|---|---|---|
| Current I | Same everywhere: I = I₁ = I₂ | Splits: I = I₁ + I₂ + … |
| Potential difference V | Splits: V = V₁ + V₂ + … | Same across each branch: V = V₁ = V₂ |
| Total resistance Rₜ | Rₜ = R₁ + R₂ + … | 1/Rₜ = 1/R₁ + 1/R₂ + … |
In a series circuit, the total resistance is larger than any individual resistor, and the total p.d. is the sum of the individual p.d.s. In a parallel circuit, the total resistance is always smaller than the smallest individual resistance, and the current from the source divides among the branches. These rules can be derived from conservation of charge (current) and conservation of energy (voltage).
在串联电路中，总电阻大于任何一个单独电阻，总电压等于各电阻电压之和。在并联电路中，总电阻总是小于最小的支路电阻，并且电源电流在各支路间分配。这些规则可以从电荷守恒（电流）和能量守恒（电压）推导得出。
5. Potential Dividers | 分压器
A potential divider is a simple circuit that uses two or more resistors in series to provide a fraction of the input voltage. For two resistors R₁ and R₂ in series across a supply voltage V_in, the output voltage across R₂ is given by V_out = V_in × (R₂ / (R₁ + R₂)). This arrangement is widely used to provide variable voltages, for instance when one of the resistors is a thermistor or an LDR.
分压器是一种利用两个或多个串联电阻从输入电压中分压的简单电路。对于串联的电阻 R₁ 和 R₂，接在电源电压 V_in 两端，R₂ 两端的输出电压为 V_out = V_in × (R₂ / (R₁ + R₂))。这种结构广泛用于提供可变电压，例如用一个热敏电阻或光敏电阻作为一个电阻时。
If a variable resistor (rheostat) is used as one element, the output can be continuously adjusted. When a sensor such as a thermistor is placed as R₂, a rise in temperature typically lowers its resistance, causing V_out to change accordingly, which can trigger switching circuits. It is important to note that the output voltage can be taken across either resistor, and the ratio determines the output value.
如果使用可变电阻器（变阻器）作为其中一个元件，输出电压可连续调节。当传感器如热敏电阻作为 R₂ 时，温度升高通常使其电阻下降，导致 V_out 相应变化，从而触发电开关电路。需要注意的是，输出电压可以取自任意一个电阻两端，其比值决定了输出值。
6. Magnetic Fields of Current-Carrying Conductors | 载流导体的磁场
A magnetic field is produced around any current-carrying conductor. For a straight wire, the field lines form concentric circles centred on the wire. The direction of the circular field can be determined by the right-hand grip rule: when the right thumb points in the direction of conventional current, the curled fingers show the field direction. The magnetic flux density B is measured in tesla (T).
任何载流导体周围都会产生磁场。对于直导线，磁力线是以导线为中心的同心圆。圆形磁场的方向可用右手螺旋定则判断：右手拇指指向约定电流方向时，弯曲的四指即表示磁场方向。磁通量密度 B 的单位是特斯拉(T)。
The magnetic field around a solenoid resembles that of a bar magnet. Inside a long solenoid, the field is uniform and parallel, while outside the field is similar to that of a dipole. The strength of the field inside a solenoid can be increased by increasing the current, the number of turns per unit length, or by inserting a soft iron core. The right-hand grip rule applies again: grip the solenoid so that the fingers follow the current, then the thumb points towards the north pole.
螺线管周围的磁场类似于条形磁铁。在长螺线管内部，磁场是均匀且平行的，外部的磁场则与磁偶极子类似。增大电流、增加单位长度上的匝数或插入软铁芯都能增强螺线管内部的磁场。右手螺旋定则同样适用：四指沿电流方向握住螺线管，拇指所指方向即为北极。
7. Magnetic Force on a Current-Carrying Conductor (Motor Effect) | 磁场对电流的作用力（电动机效应）
A conductor carrying a current in an external magnetic field experiences a force, called the motor effect. The magnitude of this force is given by F = B I L sinθ, where B is the magnetic flux density, I is the current, L is the length of conductor within the field, and θ is the angle between the current direction and the magnetic field lines. The force is maximum when θ = 90° and zero when the current is parallel to the field.
置于外部磁场中的载流导体会受到力的作用，这称为电动机效应。该力的大小由公式 F = B I L sinθ 给出，其中 B 为磁通量密度，I 为电流，L 为在磁场中的导体长度，θ 为电流方向与磁力线之间的夹角。当 θ = 90° 时力最大，电流与磁场平行时力为零。
The direction of the force can be determined using Fleming’s left-hand rule: if the thumb, first finger and second finger of the left hand are held mutually perpendicular, with the First finger in the direction of the Field, the seCond finger in the direction of the Current, then the thuMb gives the direction of the Motion (force). This rule is fundamental to the operation of electric motors and moving-coil loudspeakers.
力的方向可用弗莱明左手定则判断：伸出左手，让拇指、食指和中指两两垂直，以食指指向磁场方向（Field），中指指向电流方向（Current），则拇指所指即为运动/受力方向（Motion）。这一定则是电动机和动圈式扬声器的工作原理基础。
8. Electromagnetic Induction and Faraday’s Law | 电磁感应与法拉第定律
Electromagnetic induction occurs when there is a change in magnetic flux Φ through a circuit, inducing an e.m.f. Magnetic flux Φ = B A cosθ for a uniform field, where A is the area of the coil and θ is the angle between the field and the normal to the coil’s plane. Faraday’s law states that the magnitude of the induced e.m.f. is equal to the rate of change of flux linkage. Expressed for a coil of N turns: |ε| = N |ΔΦ / Δt|.
当穿过电路的磁通量 Φ 发生变化时，就会发生电磁感应，产生感应电动势。对于匀强磁场，磁通量 Φ = B A cosθ，其中 A 为线圈面积，θ 为磁场与线圈平面法线之间的夹角。法拉第定律指出，感应电动势的大小等于磁链的变化率。对于 N 匝线圈：|ε| = N |ΔΦ / Δt|。
Flux linkage is the product of N and Φ, so ε = -N ΔΦ / Δt when considering the direction. An e.m.f. can be induced by changing B, changing A, or changing the orientation θ of the coil relative to the field. A generator works by rotating a coil in a magnetic field, thereby continuously changing the flux linkage and producing an alternating e.m.f.
磁链是 N 与 Φ 的乘积，考虑方向时 ε = -N ΔΦ / Δt。可以通过改变 B、改变面积 A 或改变线圈相对于磁场的方位角 θ 来感应出电动势。发电机通过让线圈在磁场中旋转，持续改变磁链，从而产生交变电动势。
9. Lenz’s Law and Energy Conservation | 楞次定律与能量守恒
Lenz’s law states that the direction of an induced current is such that it opposes the change in magnetic flux that produced it. This is represented by the negative sign in ε = -N ΔΦ / Δt. The opposition ensures that energy is conserved; if the induced current helped the change, it would create energy from nothing, violating the conservation principle.
楞次定律指出，感应电流的方向总是试图阻碍引起感应电流的磁通量变化。这体现在 ε = -N ΔΦ / Δt 中的负号上。这种阻碍保证能量守恒；如果感应电流反而促进变化，就会无中生有地产生能量，违背守恒原理。
A classic example is a magnet approaching a coil: the induced current creates a magnetic field that pushes back against the magnet (repulsion), so work must be done to overcome this repulsion, converting mechanical energy to electrical energy. When the magnet is withdrawn, the induced pole attracts the magnet, again requiring work. This principle applies to eddy currents in transformer cores and braking systems.
一个经典例子是磁铁靠近线圈：感应电流产生的磁场会排斥磁铁，因此必须做功来克服排斥，将机械能转化为电能。当磁铁被抽出时，感应的极性又会吸引磁铁，同样需要做功。这一原理也适用于变压器铁芯中的涡流以及制动系统。
10. Alternating Current and Transformers | 交流电与变压器
Alternating current (AC) periodically reverses direction. The root mean square (rms) values provide a measure of the effective value of AC: V_rms = V_peak / √2 and I_rms = I_peak / √2. Household mains supply is typically AC with an rms voltage of 230 V in many regions, giving a peak voltage around 325 V. Oscilloscopes can display AC waveforms to measure peak values and period.
交流电(AC)周期性地改变方向。均方根(rms)值用于衡量交流电的有效值：V_rms = V_peak / √2，I_rms = I_peak / √2。许多地区的家用电源为交流电，有效值电压为230 V，对应的峰值电压约为325 V。示波器可显示交流波形，以测量峰值和周期。
A transformer operates on the principle of electromagnetic induction. An alternating current in the primary coil creates a varying magnetic flux in the core, which links the secondary coil and induces a varying e.m.f. For an ideal transformer, the voltage ratio equals the turns ratio: V₁ / V₂ = N₁ / N₂. Since power is conserved, I₁ V₁ ≈ I₂ V₂, so a step-up transformer increases voltage while reducing current. Real transformers experience energy losses via resistance heating, eddy currents and hysteresis, which are minimised by using low-resistance windings, laminated cores and soft magnetic materials.
变压器基于电磁感应原理工作。初级线圈中的交流电在铁芯中产生交变磁通，该磁通穿过次级线圈，感应出交变电动势。对于理想变压器，电压比等于匝数比：V₁ / V₂ = N₁ / N₂。由于功率近似守恒，I₁ V₁ ≈ I₂ V₂，因此升压变压器在升高电压的同时降低电流。实际变压器会因电阻发热、涡流和磁滞产生能量损耗，通过使用低电阻绕组、叠片铁芯和软磁材料可将损耗降至最低。
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