📚 Electricity and Magnetism for A-Level Edexcel Physics: Key Points Review | A-Level Edexcel 物理：电与磁 考点精讲
Electricity and magnetism form the backbone of classical physics and underpin much of modern technology. For Edexcel A-Level Physics, mastering both direct current (DC) circuits and the principles of electromagnetism is essential for high marks. This article breaks down the key topics, from basic current and resistance to electromagnetic induction, transformers, and essential practical investigations, with clear bilingual explanations and exam-focused formulas. Each section is designed to reinforce understanding and prepare you for typical exam questions.
电与磁是经典物理学的支柱，也是现代科技的基础。在 Edexcel A-Level 物理考试中，掌握直流电路和电磁学原理是取得高分的关键。本文将梳理从基本电流、电阻到电磁感应、变压器以及必考实验等核心考点，采用中英双语讲解，突出重点公式。每一节都旨在巩固理解，帮助你应对典型考题。
1. Electric Current and Charge | 电流与电荷
ld. Charge (Q) is measured in coulombs (C), current in amperes (A). The mathematical definition is I = ΔQ/Δt. Conventional current flows from positive to negative, opposite to electron flow.
电流 (I) 定义为电荷流动的速率。在导体中，它是在外加电场作用下自由电子的漂移。电荷 (Q) 以库仑 (C) 为单位，电流以安培 (A) 为单位。数学定义为 I = ΔQ/Δt。约定电流方向从正到负，与电子流动方向相反。
I = ΔQ / Δt
ircuit, an ammeter is connected in series to measure current, and a coulombmeter measures total charge passing through a point.
当恒定电流流经时间 t 时，转移的电荷为 Q = It。在电路中，电流表串联以测量电流，库仑计测量通过某点的总电荷量。
charge between them: V = W/Q. It is measured in volts (V). 1 volt is 1 joule per coulomb.
两点之间的电势差（电压）是将单位电荷从一点移动到另一点所做的功：V = W/Q。单位为伏特 (V)。1 伏等于 1 焦耳每库仑。
2. Ohm's Law and Resistance | 欧姆定律与电阻
nt is directly proportional to the applied voltage, so V = IR. The SI unit of resistance is the ohm (Ω).
电阻 (R) 是对电流的阻碍，由 R = V/I 给出。欧姆定律指出，在温度不变的条件下，金属导体中的电流与所加电压成正比，即 V = IR。电阻的国际单位是欧姆 (Ω)。
R = V / I
nd A cross-sectional area. Resistivity depends on temperature; for many metals, ρ increases with temperature due to increased lattice ion vibrations, making filaments in lamps non-ohmic at high temperatures.
电阻率 ρ 是决定均匀导线电阻的材料属性：R = ρL/A，其中 L 为长度，A 为横截面积。电阻率随温度变化；对多数金属而言，ρ 因晶格离子振动加剧而随温度升高，导致灯丝在高温下变为非欧姆性。
Components can be ohmic (I-V graph is a straight line through origin) or non-ohmic. For example, a filament bulb shows a curved I-V characteristic due to heating; a diode allows current in one direction only. Semiconductors like thermistors have resistance that decreases with temperature, while LDRs (light-dependent resistors) decrease resistance when light intensity increases.
元件可以是欧姆性的（I-V 图为过原点的直线）或非欧姆性的。例如，灯丝灯泡因加热呈弯曲特性；二极管只允许单向导电。半导体如热敏电阻的电阻随温度升高而下降，光敏电阻 (LDR) 在光照增强时电阻降低。
3. Electromotive Force and Internal Resistance | 电动势与内阻
ts. A real cell has internal resistance r, causing lost volts inside the source. The terminal potential difference V is given by V = ε - Ir, where I is the circuit current.
电源的电动势 (ε) 是驱动电流在全电路中流动时单位电荷所获得的能量，单位为伏特。实际电池具有内阻 r，在内部产生损耗电压。端电压 V 由 V = ε - Ir 给出，其中 I 为电路电流。
V = ε - I r
When no current flows (open circuit), the voltmeter reading equals the emf. The lost volts increase with current; at short circuit, V becomes zero and Imax nd internal resistance by varying an external load resistor, plotting V against I, where the y-intercept gives ε and the gradient gives -r.
无电流（开路）时，电压表读数等于电动势。损耗电压随电流增大而增大；短路时 V 变为零，Imax = ε/r。需要掌握通过改变外接负载电阻、绘制 V-I 图来测量电动势和内阻的方法：y 轴截距为 ε，斜率为 -r。
4. Kirchhoff's Laws | 基尔霍夫定律
Kirchhoff's first law (current law) states that the sum of currents entering any junction equals the sum of currents leaving it. This is a consequence of conservation of charge: ΣIin = ΣIout.
基尔霍夫第一定律（电流定律）：流入任一节点的电流之和等于流出该节点的电流之和，这是电荷守恒的结果：ΣIin = ΣIout。
Kirchhoff' om energy conservation. When applying the law, assign a consistent loop direction and treat emfs and p.d.s with appropriate signs.
基尔霍夫第二定律（电压定律）：在任一闭合回路中，所有电势差的代数和为零：ΣV = 0 或 Σemf = ΣIR，这源于能量守恒。应用时需指定一致的回路方向，并对电动势和电势差赋予正负号。
These laws allow analysis of complex circuits with multiple loops and power supplies. They are essential for calculating unknown currents, voltages, and the effective resistance in networks that cannot be reduced to simple series/parallel combinations.
这些定律可用于分析含多个回路和电源的复杂电路，在无法简化为简单串并联的网络中，用来计算未知电流、电压和等效电阻。
5. Potential Dividers | 电势分压器
A potential divider uses two resistors in series to provide a fraction of the input voltage. For resistors R₁ and R₂ in series across supply Vin, the output voltage across R₂ is:
电势分压器利用两个串联电阻从输入电压中取出一部分。对于跨接在电源 Vin 上的串联电阻 R₁ 和 R₂，R₂ 两端的输出电压为：
Vout = (R₂ / (R₁ + R₂)) × Vin
This principle is widely used in sensor circuits. If R₂ is a thermistor or LDR, Vout varies with temperature or light intensity. A variable resistor (potentiometer) acts as an adjustable potential divider. You may be asked to design a circuit that triggers an output when a certain condition, such as light level, is met.
这一原理广泛应用于传感器电路。若 R₂ 为热敏电阻或光敏电阻，输出电压随温度或光强变化。可变电阻器（电位计）相当于可调分压器。考题可能要求设计电路，在达到特定条件（如光照度）时触发输出。
In the context of Edexcel, you should be able to calculate the output voltage, explain the effect of replacing one resistor with a sensor, and describe how a potential divider provides a variable reference voltage for comparators or transistor switches.
在 Edexcel 考纲中，需要能够计算输出电压，解释将其中一个电阻换成传感器的影响，并描述分压器如何为比较器或晶体管开关提供可变参考电压。
6. Magnetic Fields due to Currents | 电流的磁场
: thumb points in current direction, fingers curl in direction of magnetic field lines. For a long straight conductor, the magnetic flux density at distance r is B = μ₀I/(2πr), where μ₀ is the permeability of free space.
运动的电荷或电流会产生磁场。直线导线周围的磁场方向由右手螺旋定则确定：拇指指向电流，四指弯曲方向即为磁场线。对于长直导线，距其 r 处的磁通密度为 B = μ₀I/(2πr)，其中 μ₀ 为真空磁导率。
B = μ₀ I / (2π r)
n I, where n is the number of turns per unit length. The direction can be determined by the right-hand grip rule for coils.
长螺线管内部产生匀强磁场，类似于条形磁铁。理想螺线管内部磁场强度为 B = μ₀ n I，n 为单位长度匝数。方向可用线圈的右手螺旋定则判断。
7. Magnetic Force on Currents and Charges | 磁场对电流和运动电荷的作用力
tween the field direction and the current. The force is perpendicular to both the field and the current, given by Fleming's left-hand rule.
磁场中的载流导体会受到力的作用，即电动机效应。力的大小为 F = B I L sinθ，θ 为磁场方向与电流的夹角。力的方向同时垂直于磁场和电流方向，可由弗莱明左手定则确定。
F = B I L sinθ
, causing circular motion if the velocity is perpendicular to the field. The radius of the circular path is r = m v/(B q).
对于在磁场 B 中以速度 v 运动的单个电荷 q，洛伦兹力为 F = B q v sinθ。该力始终垂直于速度，当速度与磁场垂直时，电荷做圆周运动，轨道半径 r = m v/(B q)。
These principles explain how electric motors, mass spectrometers, and particle accelerators work. In exam questions, you must be able to predict force directions, calculate magnitudes, and relate particle motion to centripetal force.
这些原理解释了电动机、质谱仪和粒子加速器的工作原理。在考题中，需要能预测力的方向，计算大小，并将粒子运动与向心力联系起来。
8. Magnetic Flux and Flux Density | 磁通量与磁通密度
eld normal, Φ = B A cosθ. Flux is measured in webers (Wb). Magnetic flux density B is the flux per unit area, measured in tesla (T).
磁通量 (Φ) 是穿过给定面积的总磁场的量度。对于匀强磁场 B 穿过与法线成 θ 角的面积 A，Φ = B A cosθ。通量单位为韦伯 (Wb)，磁通密度 B 是单位面积的通量，单位为特斯拉 (T)。
Φ = B A cosθ
The flux linkage NΦ for a coil of N turns is important in electromagnetic induction. A change in flux linkage induces an emf. Students often confuse flux density B with magnetic flux Φ; B is the field strength (vector), while Φ is the total flux (scalar).
线圈的磁通链 NΦ 在电磁感应中很重要，磁通链的变化会感应出电动势。学生常混淆磁通密度 B 和磁通量 Φ；B 是磁场强度（矢量），Φ 是总通量（标量）。
9. Electromagnetic Induction | 电磁感应
When the magnetic flux linkage through a coil changes, an electromotive force (emf) is induced. Faraday's law states that the induced emf is equal to the negative rate of change of flux linkage:
当穿过线圈的磁通链发生变化时，会感应出电动势。法拉第定律指出，感应电动势等于磁通链的负变化率：
ε = -N (ΔΦ / Δt)
Lenz's law gives the direction: the induced current flows so as to oppose the change in flux that produced it. This is why the negative sign appears. It is a direct consequence of energy conservation. You can predict the direction using the right-hand rule (generator rule).
楞次定律给出了方向：感应电流的方向总是阻碍引起感应电流的磁通量变化。这就是公式中出现负号的原因，是能量守恒的直接体现。可用右手定则（发电机定则）判断方向。
o a field B, the induced emf is ε = B L v. This is the principle behind dynamo generators.
导体切割磁场线也能产生电动势（动生电动势）。对于长度 L 的直导体以速度 v 垂直于磁场 B 运动，感应电动势 ε = B L v。这是发电机的基本原理。
ε = B L v
10. Transformers and Alternating Current | 变压器与交流电
V₀ and I₀ are peak values. For power calculations, we use root mean square (rms) values: Vrms = V₀ / √2 and Irms = I₀ / √2.
交流电 (AC) 方向周期性反转。电压和电流可表示为 V = V₀ sin(ωt) 和 I = I₀ sin(ωt)，V₀ 和 I₀ 为峰值。功率计算中使用均方根值：Vrms = V₀/√2，Irms = I₀/√2。
A transformer consists of two coils wound on a laminated soft iron core. An alternating current in the primary coil produces a changing magnetic flux, which links the secondary coil, inducing an emf. For an ideal transformer, the voltage ratio equals the turns ratio:
变压器由绕在叠片软铁芯上的两个线圈组成。初级线圈中的交流电产生变化的磁通，耦合到次级线圈，感应出电动势。理想变压器中电压比等于匝数比：
Vₛ / Vₚ = Nₛ / Nₚ
rmers increase voltage and decrease current; step-down transformers do the opposite. Transformers are used in the national grid to minimise energy losses during transmission due to ohmic heating (I²R losses).
理想变压器输入功率等于输出功率：Iₚ Vₚ = Iₛ Vₛ。升压变压器提高电压、降低电流，降压变压器则相反。变压器用于国家电网，以最大限度减少因欧姆发热 (I²R) 导致的传输能量损耗。
11. Key Practical Skills | 关键实验技能
erent lengths, plot R against L, and use the gradient = ρ/A. Ensure the wire is kept at constant temperature by using a low current and switching off between readings.
Edexcel 实验评估要求测量电阻率。测定金属丝的电阻率需测量不同长度下的电阻，绘制 R-L 图，斜率 = ρ/A。须用较小电流并在读数间歇断电，以保持恒温。
rcept gives ε, and the gradient is -r. Always include a switch to avoid draining the cell.
测量电池内阻时，搭建含可变电阻的电路，记录 V 和 I，利用线性方程 V = ε - rI，截距为 ε，斜率为 -r。必须使用开关，避免电池耗尽。
Investigating magnetic field patterns using iron filings and plotting compasses, observing electromagnetic induction with a magnet and coil connected to a centre-zero galvanometer, and measuring the efficiency of a transformer are common required practicals. Precision, safety (especially thermal and electrical hazards), and careful recording are key.
用铁屑和小磁针描绘磁场线、用磁铁和接中心零位检流计的线圈观察电磁感应、测量变压器效率等都是常见的必做实验。精度、安全（特别是热和电危害）以及仔细记录是关键。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图