📚 Electricity and Magnetism: Key Concepts Revision | 电与磁：考点精讲
Electricity and magnetism form the cornerstone of physics in the IB and WJEC science curricula. Understanding how charges move, how circuits behave, and how magnetic fields interact with currents is vital for success in both theoretical and practical assessments. This revision guide breaks down the essential points you need to master, from fundamental definitions to real-world applications like transformers and generators.
电与磁是 IB 和 WJEC 科学课程中物理学的基石。理解电荷如何运动、电路如何工作以及磁场如何与电流相互作用，对理论和实践考核都至关重要。本复习指南将你需要掌握的核心考点逐一分解，从基本定义到变压器和发电机等实际应用，帮助你系统巩固。
1. Electric Charge and Current | 电荷与电流
Electric charge is a fundamental property of matter, existing in two types: positive and negative. Like charges repel, while opposite charges attract. The SI unit of charge is the coulomb (C), and the charge on a single electron is approximately −1.60 × 10⁻ⁱ⁹ C.
电荷是物质的基本属性，分为正电荷和负电荷两种。同种电荷相互排斥，异种电荷相互吸引。电荷的国际单位是库仑 (C)，单个电子的电荷约为 −1.60 × 10⁻ⁱ⁹ C。
Electric current is the rate of flow of charge. It is measured in amperes (A), where 1 A = 1 C s⁻¹. In a metallic conductor, current is carried by moving electrons, which flow from the negative terminal to the positive terminal of a power supply. However, conventional current is taken as the direction of positive charge flow, opposite to electron movement.
电流是电荷流动的速率，以安培 (A) 为单位，1 A = 1 C s⁻¹。在金属导体中，电流由移动的电子携带，电子从电源的负极流向正极。但习惯上规定正电荷移动的方向为电流方向，与电子移动方向相反。
To measure current, an ammeter must be connected in series with the component. In a series circuit, the current remains the same at all points. In a parallel circuit, the total current from the source divides among the branches and then recombines.
测量电流时，安培表必须与被测元件串联。在串联电路中，各处电流相等。在并联电路中，总电流在支路中分流，然后汇合。
2. Voltage, Resistance and Ohm’s Law | 电压、电阻与欧姆定律
Voltage, or potential difference, is the energy transferred per unit charge between two points in a circuit. It is measured in volts (V), where 1 V = 1 J C⁻¹. A voltmeter is always connected in parallel across the component being tested.
电压即电势差，是电路中两点间单位电荷转移的能量，以伏特 (V) 为单位，1 V = 1 J C⁻¹。电压表必须与被测元件并联。
Resistance is a measure of how much a component opposes the flow of current. It is defined as R = V / I and is measured in ohms (Ω). Ohm’s law states that, at constant temperature, the current through a conductor is directly proportional to the potential difference across it, provided physical conditions remain unchanged.
电阻衡量元件对电流的阻碍作用，定义为 R = V / I，单位是欧姆 (Ω)。欧姆定律指出，在温度不变的条件下，导体中的电流与它两端的电压成正比，前提是物理条件保持不变。
V = I × R
Ohmic conductors obey Ohm’s law, displaying a linear voltage-current graph. Non-ohmic conductors, such as diodes and filament lamps, do not have a constant resistance; their V–I graphs are curved due to heating effects or semiconduction behaviour.
欧姆导体遵守欧姆定律，其电压-电流图呈线性。非欧姆导体如二极管和灯丝灯泡，其电阻不是常量；由于热效应或半导体特性，它们的 V-I 图线是弯曲的。
Factors affecting resistance include length (R ∝ L), cross-sectional area (R ∝ 1/A), temperature (for metals, resistance increases with temperature), and the material’s resistivity ρ. Resistance can be calculated using the equation:
影响电阻的因素有长度 (R ∝ L)、横截面积 (R ∝ 1/A)、温度（对大多数金属，温度升高电阻增大）以及材料的电阻率 ρ。电阻可通过公式计算：
R = ρ × (L / A)
3. Series and Parallel Circuits | 串联与并联电路
In a series circuit, components are connected end-to-end, providing a single path for current. The total resistance is the sum of individual resistances:
在串联电路中，元件首尾相连，电流只有一条通路。总电阻等于各电阻之和：
Rtotal = R₁ + R₂ + R₃ + …
The current is the same through all components, and the supply voltage is divided among them in proportion to their resistances. This arrangement is used for controlling current and in voltage divider circuits.
串联电路中各处电流相同，电源电压按电阻比例分配到各元件。这种连接方式用于控制电流和分压电路。
In a parallel circuit, components are connected across common points, providing multiple paths. The total resistance is found using the reciprocal formula:
在并联电路中，元件并接在公共点之间，提供多条路径。总电阻用倒数公式计算：
1 / Rtotal = 1 / R₁ + 1 / R₂ + 1 / R₃ + …
The potential difference across each branch is equal to the supply voltage, while the total current is the sum of the branch currents. Household wiring uses parallel connections so that appliances can operate independently.
各支路两端的电压相等且等于电源电压，而总电流等于各支路电流之和。家庭电路采用并联连接，使电器能够独立工作。
| Property | Series | Parallel |
|---|---|---|
| Current (I) | Same everywhere | Splits among branches |
| Voltage (V) | Divided across components | Same across each branch |
| Total resistance | Larger than largest resistor | Smaller than smallest resistor |
4. Electrical Power and Energy | 电功率与电能
Electrical power is the rate at which energy is transferred or converted in a circuit. It is measured in watts (W). The power dissipated in a component can be calculated using any of the following equations derived from Ohm’s law:
电功率是电路中能量转移或转换的速率，单位是瓦特 (W)。元件消耗的功率可用以下由欧姆定律导出的公式计算：
P = I × V
P = I² × R
P = V² / R
The energy transferred is the product of power and time. Energy (in joules) = power × time. In domestic electricity use, energy is often measured in kilowatt-hours (kWh), where 1 kWh is the energy consumed by a 1 kW device operating for one hour.
转移的能量等于功率与时间的乘积。能量 (焦耳) = 功率 × 时间。在家庭用电中，电能常用千瓦时 (kWh) 计量，1 kWh 表示功率为 1 kW 的设备工作一小时所消耗的能量。
Efficiency of electrical devices can be determined by the ratio of useful output power to total input power. High-efficiency devices waste less energy as heat, making them more economical and environmentally friendly.
电器设备的效率可用有用输出功率与总输入功率之比来评价。高效率设备以热能形式浪费的能量较少，更经济环保。
5. Magnetism Fundamentals | 磁学基础
Magnetism arises from moving electric charges, primarily electrons spinning and orbiting within atoms. A magnetic material such as iron, nickel, or cobalt contains domains—small regions where atomic magnetic moments align. When these domains are aligned by an external field, the material becomes magnetised.
磁性源于运动的电荷，主要是原子内部电子的自旋和轨道运动。铁、镍、钴等磁性材料含有磁畴——原子磁矩排列一致的小区域。当外加磁场使磁畴取向一致时，材料就被磁化。
A permanent magnet retains its magnetism because its domains remain locked in alignment. Magnetic field lines, invisible but mapped by compasses or iron filings, run from the north pole to the south pole outside the magnet and form closed loops. The field is strongest where lines are closest together.
永磁体因其磁畴保持锁定排列而能长期保留磁性。磁感线虽然看不见，但可用指南针或铁屑显示，在磁体外部从北极指向南极，形成闭合回路。磁感线越密集的区域磁场越强。
The Earth itself behaves as a giant magnet with a magnetic axis roughly aligned with its rotational axis, giving rise to the geomagnetic field that protects us from solar wind particles and aids navigation.
地球本身就像一个巨大的磁体，其磁轴大致与自转轴对齐，产生地磁场，保护我们免受太阳风粒子的侵害，并用于导航。
6. Electromagnetism and Right-Hand Rules | 电磁学与右手定则
When an electric current flows through a conductor, it produces a magnetic field around it. For a straight wire, the magnetic field lines are concentric circles. The direction of this field can be determined using the right-hand grip rule: point the thumb of your right hand in the direction of conventional current, and your curled fingers indicate the direction of the magnetic field.
当电流流经导体时，会在其周围产生磁场。对于直导线，磁感线为同心圆。磁场方向可用右手握线定则判断：右手拇指指向电流方向，弯曲的四指则指向磁场方向。
A coil of wire (solenoid) produces a magnetic field similar to that of a bar magnet when a current passes through it. The right-hand rule for a solenoid states that if you curl the fingers of your right hand in the direction of current around the coil, your thumb points toward the north pole. The strength of the solenoid’s field can be increased by adding an iron core, increasing the current, or increasing the number of turns.
通电线圈（螺线管）产生的磁场与条形磁铁相似。右手螺旋定则指出，右手弯曲四指指向线圈中的电流方向，拇指所指即为北极。在螺线管中加入铁芯、增大电流或增加匝数都能增强其磁场。
Electromagnets, temporary magnets created by current-carrying coils wrapped around a soft iron core, are widely used in relays, electric bells, and magnetic cranes because their magnetism can be switched on and off easily.
电磁铁是由绕在软铁芯上的载流线圈形成的暂时磁体，广泛应用于继电器、电铃和电磁起重机中，因为其磁性能方便地通断控制。
7. The Motor Effect (Left-Hand Rule) | 电动机效应（左手定则）
A current-carrying wire placed in an external magnetic field experiences a force. This is called the motor effect. The force is maximum when the current is perpendicular to the field lines, and zero when it is parallel. The magnitude of the force can be calculated using:
通电导线置于外部磁场中会受到力的作用，这称为电动机效应。当电流与磁感线垂直时力最大，平行时力为零。力的大小可用下式计算：
F = B × I × L
where F is force (N), B is magnetic flux density (T), I is current (A), and L is the length of conductor in the field (m). The direction of force is given by Fleming’s left-hand rule: hold the thumb, first finger, and second finger mutually at right angles. The First finger represents Field direction (N to S), the seCond finger represents Current direction (conventional), and the ThuMb represents Motion (force) direction.
其中 F 是作用力 (N)，B 是磁通密度 (T)，I 是电流 (A)，L 是导体在磁场中的有效长度 (m)。力的方向用弗莱明左手定则判断：将拇指、食指和中指相互垂直。食指表示磁场方向 (N→S)，中指表示电流方向，拇指表示导体运动（受力）方向。
The motor effect is the principle behind the simple DC electric motor. A rectangular coil rotating in a magnetic field experiences turning forces (torques). A split-ring commutator reverses the current every half-turn, ensuring continuous rotation in one direction.
电动机效应是直流电动机的基本原理。矩形线圈在磁场中旋转时受到力矩作用。换向器每半圈改变电流方向，确保线圈连续沿同一方向转动。
8. Electromagnetic Induction | 电磁感应
Electromagnetic induction is the process by which a changing magnetic field induces an electromotive force (emf) and current in a conductor. This phenomenon was discovered by Michael Faraday and is the basis for generating electricity.
电磁感应是指变化的磁场在导体中产生电动势（emf）和电流的过程。这一现象由法拉第发现，是发电的基础。
Faraday’s law states that the magnitude of the induced emf is directly proportional to the rate of change of magnetic flux linkage. Lenz’s law gives the direction of the induced current: it always opposes the change that produced it. This is a consequence of conservation of energy.
法拉第定律指出，感应电动势的大小与磁通链的变化率成正比。楞次定律给出了感应电流的方向：它总是阻碍引起感应的变化。这是能量守恒的结果。
Induction can be demonstrated by moving a magnet in and out of a coil, or by moving a conductor across magnetic field lines. Faster movement, stronger magnets, and more coil turns all increase the induced emf. Applications include dynamos, induction cookers, and wireless charging systems.
让磁铁在线圈中进出运动，或让导体切割磁感线，均可演示电磁感应。磁铁移动越快、磁场越强、线圈匝数越多，感应电动势越大。应用包括发电机、电磁炉和无线充电等。
9. Generators and Alternators | 发电机与交流发电机
A generator converts mechanical energy into electrical energy using electromagnetic induction. A simple AC generator (alternator) consists of a coil rotating in a magnetic field. As the coil rotates, the magnetic flux linkage changes sinusoidally, inducing an alternating emf. Slip rings and brushes connect the coil to the external circuit without reversing the connections, producing an alternating current (AC).
发电机利用电磁感应将机械能转化为电能。简单的交流发电机由在磁场中转动的线圈构成。线圈转动时，磁通链按正弦规律变化，产生交变电动势。滑环和电刷在不改变连接极性的情况下将线圈与外部电路相连，输出交流电。
A DC generator uses a split-ring commutator instead of slip rings, which rectifies the current so that it flows in one direction only. The DC output is not smooth, but pulsing. The frequency of the ac output is equal to the number of coil rotations per second.
直流发电机用换向器代替滑环，将电流整流为单向流动。直流输出是脉动的而非平滑的。交流电的频率等于线圈每秒转动的圈数。
The magnitude of the generated emf can be increased by using stronger magnets, rotating the coil faster, using more turns of wire, or adding a soft iron core to concentrate the magnetic field.
要增大感应电动势，可使用更强的磁铁、加快线圈转速、增加线圈匝数，或加入软铁芯来集中磁场。
10. Transformers and Power Transmission | 变压器与电力传输
A transformer is a device that changes the voltage of an alternating current supply. It consists of two coils, the primary and secondary, wound on a laminated soft iron core. An alternating current in the primary coil produces a changing magnetic field, which induces an emf in the secondary coil through mutual induction.
变压器是改变交流电电压的装置，由绕在叠片软铁芯上的两个线圈——初级线圈和次级线圈组成。初级线圈中的交变电流产生变化的磁场，通过互感在次级线圈中感应出电动势。
For an ideal transformer, the ratio of voltages equals the ratio of the number of turns:
对于理想变压器，电压之比等于匝数之比：
Vp / Vs = Np / Ns
Assuming 100% efficiency, the power in the primary coil equals the power in the secondary coil, so:
假设效率为 100%，初级线圈的功率等于次级线圈的功率，因此：
Vp × Ip = Vs × Is
Step-up transformers increase voltage (more turns on secondary), while step-down transformers decrease voltage (more turns on primary). These are crucial in national grid systems: electricity is transmitted at very high voltages to reduce energy lost as heat due to the I²R loss in transmission lines, then stepped down to safe voltages for homes and industry.
升压变压器增加电压（次级匝数多），降压变压器降低电压（初级匝数多）。这两种变压器在国家电网中至关重要：电力以极高电压传输以减少输电线路 I²R 热损耗，随后降压至家庭和工业安全使用的电压。
Real transformers are not 100% efficient due to resistive heating in coils (copper losses), eddy currents in the core, hysteresis loss, and leakage flux. Laminating the core and using low-resistance wire reduce these losses.
实际变压器并非 100% 高效，原因包括线圈电阻发热（铜损）、铁芯中的涡流、磁滞损耗以及漏磁。采用叠片铁芯和低电阻导线可以减少这些损耗。
11. Magnetic Forces on Charged Particles | 磁场对带电粒子的作用
When a charged particle moves through a magnetic field, it experiences a force perpendicular to both its velocity and the field. This force, known as the Lorentz force, causes the particle to follow a circular path if the velocity is perpendicular to a uniform magnetic field. The magnitude of the force is given by:
带电粒子在磁场中运动时，会受到一个既垂直于速度又垂直于磁场的力。这个力称为洛伦兹力，如果速度与匀强磁场垂直，粒子将做圆周运动。力的大小为：
F = B × q × v
where q is the charge and v is the speed of the particle. The direction is determined by Fleming’s left-hand rule, remembering that the current direction is opposite to electron flow. This principle is exploited in devices such as mass spectrometers, cathode ray tubes, and particle accelerators.
其中 q 是电荷量，v 是粒子的速度。方向由弗莱明左手定则判断，注意电子的电流方向与其运动方向相反。这一原理应用于质谱仪、阴极射线管和粒子加速器等设备。
The radius r of the circular path can be derived by equating the magnetic force to the centripetal force required for circular motion:
圆形路径的半径 r 可由磁力等于向心力推导：
B × q × v = m × v² / r ⇒ r = m × v / (B × q)
This relationship shows that greater mass or speed increases the radius, while a stronger field or larger charge reduces it. In a cyclotron, this principle allows particles to be accelerated to high energies for research and medical applications.
此关系表明，较大的质量或速度会使半径增大，而更强的磁场或更大的电荷会使半径减小。在回旋加速器中，这一原理使粒子加速到高能，用于研究和医疗。
12. Safety, Practical Skills and Exam Tips | 安全、实验技能与应试技巧
When investigating electric circuits and magnetism, always follow safety protocols: never exceed component ratings, avoid short circuits, and disconnect power before modifying a circuit. Use ammeters in series and voltmeters in parallel; always start with the highest range to avoid damage. In magnetism experiments, keep magnets away from sensitive electronics and allow iron filings to be cleaned up safely.
探究电路与磁学实验时，务必遵守安全规程：切勿超出元件额定值、避免短路、改动电路前先断开电源。安培表串联、电压表并联；始终从最高量程开始以防损坏。在磁学实验中，使磁铁远离敏感电子设备，并安全清理铁屑。
Graph plotting and analysis are frequent in exams. Ensure you can plot V–I graphs for ohmic and non-ohmic conductors, and interpret the gradient to find resistance. For a diode, the threshold voltage where current sharply increases is a key feature. Understanding the shape of magnetic field lines for different configurations—straight wire, solenoid, and bar magnet—is essential.
考试中常要求绘图和分析。确保能绘制欧姆导体和非欧姆导体的 V-I 图，并通过斜率求电阻。对于二极管，电流急剧增加时的阈值电压是关键特征。理解直导线、螺线管和条形磁铁的磁感线形状也是必需的。
Numerical problems often combine multiple concepts, such as using Ohm’s law, power equations, and transformer turns ratio. Unit conversion is critical: remember 1 mA = 10⁻³ A, 1 kV = 10³ V. Use consistent SI units to avoid errors. In transformer calculations, if efficiency is not 100%, output power = efficiency × input power.
计算题常综合多知识点，如欧姆定律、功率公式、变压器匝数比。单位换算至关重要：牢记 1 mA = 10⁻³ A，1 kV = 10³ V。统一使用 SI 单位避免出错。变压器计算中，若效率非 100%，输出功率 = 效率 × 输入功率。
Finally, for extended response questions, structure your answer to include definitions, relevant equations, and real-world applications. For instance, when explaining how a loudspeaker works, connect the motor effect, alternating current, and vibration of the cone. Demonstrate the ability to link topics coherently to earn top marks.
最后，对于简答题或论述题，组织答案时要包含定义、相关公式和实际应用。例如，解释扬声器工作原理时，要结合电动机效应、交流电和纸盆振动。展现连贯关联不同主题的能力，才能赢得高分。
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