📚 A-Level CIE Physics: Electricity and Magnetism Key Points | A-Level CIE 物理：电与磁考点精讲
Electricity and magnetism form the backbone of A-Level Physics, linking fundamental concepts such as electric fields, circuits, and electromagnetic induction. This revision guide walks you through the core topics prescribed by the CIE syllabus, with paired explanations in English and Chinese to reinforce understanding. Each section highlights essential definitions, formulas, and typical problem-solving approaches, ensuring you are well prepared for both structured questions and multiple-choice assessments.
电和磁构成了 A-Level 物理的核心，将电场、电路和电磁感应等基本概念联系在一起。本篇复习指南带你梳理 CIE 考纲规定的核心主题，提供英文与中文的成对解释以加深理解。每一节都着重强调关键定义、公式和典型解题思路，确保你为结构题和选择题做好充分准备。
1. Electric Field and Coulomb's Law | 电场与库仑定律
An electric field is a region in which a stationary charge experiences an electric force. The electric field strength E at a point is defined as the force per unit positive charge placed at that point, expressed as E = F/q. Its SI unit is newtons per coulomb (N C⁻¹) or, equivalently, volts per metre (V m⁻¹).
电场是静止电荷会受电力的区域。某点的电场强度 E 定义为放在该点的单位正电荷所受的力，表示为 E = F/q，其 SI 单位是牛每库仑（N C⁻¹）或等价的伏每米（V m⁻¹）。
F = (1/(4πε₀))(|Q₁Q₂|/r²)
Coulomb' rmittivity of free space (8.85 × 10⁻¹² F m⁻¹). The force is attractive for unlike charges and repulsive for like charges, and it obeys an inverse‑square relationship with distance.
库仑定律给出真空中相距 r 的两个点电荷 Q₁ 和 Q₂ 之间的静电力大小。常数 ε₀ 是真空介电常数（8.85 × 10⁻¹² F m⁻¹）。异种电荷相吸引，同种电荷相排斥，且该力与距离平方成反比。
2. Electric Potential and Potential Energy | 电势与电势能
Electric potential V at a point is the work done per unit positive charge in bringing a test charge from infinity to that point without acceleration. The potential due to a point charge Q at a distance r is given by V = Q/(4πε₀r). Potential is a scalar quantity measured in volts (V).
某点的电势 V 是将单位正电荷从无穷远无加速地移到该点所做的功。点电荷 Q 在距离 r 处产生的电势为 V = Q/(4πε₀r)。电势是标量，单位为伏特（V）。
V = Q/(4πε₀r)
Electric potential energy U between two point charges Q₁ and Q₂ separated by r is U gy depends on the signs of the charges: it is positive for like charges (repulsive) and negative for unlike charges (attractive).
两点电荷 Q₁ 和 Q₂ 相距 r 时的电势能 U 为 U = Q₁Q₂/(4πε₀r)。该能量的正负取决于电荷的正负：同号为正（排斥），异号为负（吸引）。
3. Capacitance and Capacitors | 电容与电容器
Capacitance C is the charge stored per unit potential difference across a capacitor: C = Q/V. The SI unit is the farad (F). A parallel‑plate capacitor of plate area A and separation d with a dielectric of permittivity ε has capacitance C = εA/d.
电容 C 是电容器两端每单位电势差所储存的电荷：C = Q/V。SI 单位是法拉（F）。两块面积为 A、间距为 d 且填充介电常数为 ε 的电介质的平行板电容器，其电容为 C = εA/d。
C = Q/V ; C = εA/d
Energy stored in a capacitor can be expressed in three equivalent forms: W = ½QV = ½CV² = ½Q²/C. Capacitors charge and discharge exponentially through a resistor with time constant τ = RC, where R is the resistance in the circuit.
储存在电容器中的能量可用三种等价形式表示：W = ½QV = ½CV² = ½Q²/C。电容器通过电阻充放电呈指数变化，时间常数 τ = RC，其中 R 是电路中的电阻。
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, measured in amperes (A). By convention, the direction of current is taken as the direction of flow of positive charge. In metals, however, it is electrons that move in the opposite direction.
电流 I 是电荷的流动速率：I = ΔQ/Δt，单位为安培（A）。按惯例，电流方向取正电荷流动的方向；但在金属中，实际移动的是电子，方向相反。
Ohm's law states that the potential difference V across a conductor is directly proportional to the current I flowing through it, provided the temperature remains constant: V = IR, where R is the resistance in ohms (Ω). Resistance arises due to collisions between conduction electrons and lattice ions.
欧姆定律指出，在温度不变的条件下，导体两端电势差 V 与流过它的电流 I 成正比：V = IR，其中 R 是电阻，单位为欧姆（Ω）。电阻来源于传导电子与晶格离子间的碰撞。
R = ρL/A
The resistivity ρ of a material relates resistance to the conductor's length L and cross‑sectional area A. Resistivity depends on the material and its temperature; metals have low resistivity, while insulators have very high resistivity.
材料的电阻率 ρ 将电阻与导体长度 L 和截面积 A 联系起来。电阻率取决于材料及其温度；金属电阻率低，绝缘体电阻率很高。
5. DC Circuits and Kirchhoff's Laws | 直流电路与基尔霍夫定律
Kirchhoff's first law (junction rule) is a statement of conservation of charge: the total current entering a junction equals the total current leaving it. Kirchhoff's second law (loop rule) derives from conservation of energy: the sum of the electromotive forces (emfs) around any closed loop equals the sum of the potential drops (IR) across components in that loop.
基尔霍夫第一定律（节点定则）是电荷守恒的表述：流入节点的总电流等于流出节点的总电流。基尔霍夫第二定律（回路定则）源于能量守恒：沿任一闭合回路的电动势代数和等于该回路中各元件上电压降（IR）的代数和。
ΣIin = ΣIout ; Σε = ΣIR
In series circuits, the current is the same through all components, and the total resistance is the sum of individual resistances: R_total = R₁ + R₂ + ... In parallel circuits, the potential difference is the same across each branch, and the reciprocal of total resistance is the sum of reciprocals: 1/R_total = 1/R₁ + 1/R₂ + ...
在串联电路中，通过所有元件的电流相同，总电阻等于各电阻之和：R_总 = R₁ + R₂ + ... 在并联电路中，各支路两端电压相等，总电阻的倒数为各电阻倒数之和：1/R_总 = 1/R₁ + 1/R₂ + ...
Potential divider circuits are widely used to provide a variable voltage from a fixed source. The output voltage across one resistor in a series chain is V_out = (R₂/(R₁ + R₂)) × V_in. This principle appears in sensors, volume controls, and many practical circuits.
分压电路广泛用于从固定电源中获取可变电压。串联链中一个电阻两端的输出电压为 V_out = (R₂/(R₁ + R₂)) × V_in。这一原理应用于传感器、音量控制及许多实际电路中。
6. Magnetic Fields and Forces on Moving Charges | 磁场与运动电荷受力
A magnetic field is a region where moving charges or magnetic materials experience a force. The direction of the magnetic field is the direction in which the north pole of a compass needle points. Magnetic field lines are continuous and form closed loops; they emerge from the north pole of a magnet and enter the south pole.
磁场是运动电荷或磁性材料受力的区域。磁场方向是罗盘指北极所指的方向。磁感线是连续的闭合曲线；它们从磁体的北极发出，进入南极。
F = q v B sinθ
When a charge q moves with velocity v through a magnetic field of flux density B, it experiences a magnetic force F. The magnitude depends on the angle θ between v and B. The direction of the force is given by Fleming's left‑hand rule for a positive charge (reversed for a negative charge).
当电荷 q 以速度 v 在磁通密度为 B 的磁场中运动时，会受到磁力 F。其大小取决于 v 与 B 间的夹角 θ。正电荷的受力方向由弗莱明左手定则确定（负电荷相反）。
This force is always perpendicular to both v and B, so it does no work on the charge; it only changes the direction of motion, causing the charge to follow a circular or helical path if v is perpendicular to a uniform B field.
该力始终垂直于 v 和 B，因此对电荷不做功；它只改变运动方向。若 v 垂直于均匀磁场 B，电荷将作圆周或螺旋运动。
7. Magnetic Force on a Current-Carrying Conductor | 载流导体在磁场中的受力
A current‑carrying conductor placed in a magnetic field experiences a force. This is the macroscopic result of the magnetic forces acting on the individual moving charges inside the conductor. For a straight wire of length L carrying current I at an angle θ to a uniform magnetic field B, the force is given by F = BIL sinθ.
放在磁场中的载流导体会受到力。这是作用在导体内各个运动电荷上的磁力的宏观表现。对于长 L、载电流 I 且与均匀磁场 B 成夹角 θ 的直导线，受力为 F = BIL sinθ。
F = B I L sinθ
Fleming's left‑hand rule again determines the direction of the force: thumb points in the direction of force, index finger in the direction of magnetic field, and middle finger in the direction of conventional current. This principle is applied in electric motors, loudspeakers, and moving‑coil instruments.
弗莱明左手定则同样可判定力方向：拇指指向受力方向，食指指向磁场方向，中指指向常规电流方向。这一原理应用于电动机、扬声器和动圈式仪表中。
8. Electromagnetic Induction and Faraday's Law | 电磁感应与法拉第定律
Electromagnetic induction occurs when the magnetic flux linking a circuit changes, producing an induced emf. This is the fundamental principle behind generators and transformers. The induced emf in a coil of N turns is proportional to the rate of change of magnetic flux Φ through the coil.
当穿过电路的磁通量发生变化时，就会发生电磁感应，产生感应电动势。这是发电机和变压器背后的基本原理。线圈（共 N 匝）中感应出的电动势与穿过线圈的磁通量 Φ 的变化率成正比。
ε = –N (ΔΦ/Δt)
Faraday' emf equals the rate of change of magnetic flux linkage. Magnetic flux Φ is defined as Φ = BA cosθ, where B is the magnetic flux density, A is the area, and θ is the angle between the field and the normal to the area. Flux linkage is NΦ.
法拉第电磁感应定律指出，感应电动势的大小等于磁链的变化率。磁通量 Φ 定义为 Φ = BA cosθ，其中 B 为磁通密度，A 为面积，θ 是磁场与面积法线间的夹角。磁链则为 NΦ。
If a conductor of length L moves with velocity v perpendicular to a uniform magnetic field B, the induced emf is ε = BLv. This result follows directly from Faraday's law for a moving conductor cutting magnetic field lines.
若长为 L 的导体以速度 v 垂直于均匀磁场 B 运动，感应电动势为 ε = BLv。该结果直接由法拉第定律导出，适用于导体切割磁感线的情况。
9. Lenz's Law and Induced EMF | 楞次定律与感应电动势
Lenz's law gives the direction of the induced emf and current: the induced current flows in such a direction as to oppose the change in magnetic flux that produced it. The minus sign in Faraday's law represents this physical principle. Lenz's law is a manifestation of the conservation of energy.
楞次定律给出感应电动势和感应电流的方向：感应电流的流向总是试图阻碍产生它的磁通量变化。法拉第定律中的负号正是这一物理原理的体现。楞次定律是能量守恒的表现。
For example, if a bar magnet's north pole is pushed into a coil, the induced current produces a north pole at the coil end facing the magnet, thereby repelling it and opposing the increase in flux. When the magnet is withdrawn, the induced current reverses to create a south pole, attracting the magnet back and opposing the flux decrease.
例如，若条形磁铁的北极推入线圈，感应电流使线圈朝向磁铁的一端形成北极，从而排斥磁铁，阻碍磁通增加。当磁铁抽出时，感应电流反转，产生南极，吸引磁铁返回，阻碍磁通减少。
This opposition is key to understanding back emf in motors and the damping effects in galvanometers. Eddy currents, circulating currents induced in bulk conductors by changing magnetic fields, also follow Lenz's law and are utilised in induction braking and metal detectors.
这种“对抗”特性是理解电动机反电动势和检流计阻尼效应的关键。涡流是变化磁场在块状导体中感应出的环流，同样遵从楞次定律，被应用于感应制动和金属探测器中。
10. Transformers and Energy Transmission | 变压器与电能输送
A transformer consists of two coils wound on a common soft‑iron core. An alternating current in the primary coil produces a changing magnetic flux in the core, which links the secondary coil and induces an alternating emf. For an ideal transformer with no energy losses, the ratio of secondary to primary voltages equals the ratio of the turns: Vₛ/Vₚ = Nₛ/Nₚ.
变压器由绕在同一软铁芯上的两个线圈组成。一次线圈中的交流电在铁芯中产生变化磁通，该磁通穿过二次线圈，感应出交流电动势。对于无能量损耗的理想变压器，二次与一次电压之比等于匝数比：Vₛ/Vₚ = Nₛ/Nₚ。
Vₛ/Vₚ = Nₛ/Nₚ ; Iₛ/Iₚ = Nₚ/Nₛ
Power input equals power output for an ideal transformer: VₚIₚ = VₛIₛ. This leads to the inverse relationship for currents: Iₛ/Iₚ = Nₚ/Nₛ. Step‑up transformers increase voltage and decrease current, while step‑down transformers do the opposite, enabling efficient long‑distance power transmission.
理想变压器输入功率等于输出功率：VₚIₚ = VₛIₛ。由此可得电流的反比关系：Iₛ/Iₚ = Nₚ/Nₛ。升压变压器升高电压、降低电流；降压变压器则相反，从而实现了高效远距离输电。
Real transformers experience losses due to resistance heating in the coils (copper loss), eddy currents in the core, and hysteresis in the magnetic material. Laminated cores, soft magnetic materials with narrow hysteresis loops, and low‑resistance windings minimise these losses.
实际变压器存在损耗，包括线圈电阻发热（铜损）、铁芯中的涡流损耗以及磁性材料的磁滞损耗。采用叠片铁芯、窄磁滞回线的软磁材料和低电阻绕组可以最大限度地减少这些损耗。
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