📚 Electricity and Magnetism: Key Concepts for IB and Edexcel | 电与磁：IB 及 Edexcel 考点精讲
Electricity and magnetism form the backbone of classical physics, and for students preparing for IB or Edexcel assessments, a solid grasp of these topics is essential. This article covers the most tested concepts, from electric charge to electromagnetic induction, with bilingual explanations to support your revision.
电与磁是经典物理学的支柱，对于准备 IB 或 Edexcel 考试的学生而言，牢固掌握这些主题至关重要。本文涵盖了从电荷到电磁感应等最常考的概念，并以双语解释助力复习。
1. Electric Charge and Coulomb’s Law | 电荷与库仑定律
Charge is a fundamental property of matter. There are two types: positive and negative. Like charges repel, unlike charges attract. The unit of charge is the coulomb (C). The magnitude of the force between two point charges is given by Coulomb’s law:
电荷是物质的基本属性，分正、负两种。同性电荷相斥，异性电荷相吸。电荷的单位是库仑 (C)。两点电荷间作用力的大小由库仑定律给出：
F = k |q₁ q₂| / r²
where k = 8.99 × 10⁹ N·m²/C² in a vacuum. The force acts along the line joining the charges.
其中真空里 k = 8.99 × 10⁹ N·m²/C²，力的方向沿两电荷连线。
In IB and Edexcel, you are expected to calculate the resultant force when more than two charges are present, using vector addition. The principle of superposition applies: the net force on a charge is the vector sum of the forces from all other charges.
在 IB 和 Edexcel 考试中，要求计算多个电荷存在时的合力，使用矢量加法。叠加原理适用：某电荷受到的净力等于所有其他电荷对其作用力的矢量和。
2. Electric Fields and Potential | 电场与电势
An electric field E is a region where a charge experiences a force. It is defined as E = F / q. The field lines point away from positive charges and toward negative charges. For a uniform field between parallel plates: E = V / d, where V is the potential difference and d is the plate separation.
电场 E 是电荷受力的区域，定义为单位正电荷所受的力，即 E = F / q。电场线从正电荷出发，指向负电荷。平行板间的匀强电场：E = V / d，V 为电势差，d 为板间距。
Electric potential V at a point is the work done per unit charge to bring a positive test charge from infinity to that point. For a point charge: V = kQ / r. Potential difference drives current in circuits.
电势 V 是把单位正电荷从无限远移至该点所做的功。点电荷电势：V = kQ / r。电势差驱动电路中的电流。
3. Current, Voltage and Resistance | 电流、电压与电阻
Electric current I is the rate of flow of charge: I = ΔQ / Δt, measured in amperes (A). Conventional current flows from positive to negative. Potential difference (voltage) V is the energy transferred per unit charge: V = W / Q, measured in volts (V). Resistance R opposes current flow, measured in ohms (Ω).
电流 I 是电荷流动的速率：I = ΔQ / Δt，单位为安培 (A)。传统电流方向从正到负。电势差（电压）V 是单位电荷转移的能量：V = W / Q，单位为伏特 (V)。电阻 R 阻碍电流，单位为欧姆 (Ω)。
Resistance depends on material, length L, cross-sectional area A, and temperature. Resistivity ρ links these: R = ρL / A. Conductors have low ρ; insulators have high ρ.
电阻取决于材料、长度 L、截面积 A 及温度。电阻率 ρ 的关系式：R = ρL / A。导体的 ρ 低，绝缘体的 ρ 高。
4. Ohm’s Law and Resistivity | 欧姆定律与电阻率
Ohm’s law states that for many conductors at constant temperature, the current through a component is directly proportional to the potential difference across it: V = IR. The I–V characteristic for an ohmic conductor is a straight line through the origin.
欧姆定律指出，恒温下许多导体的电流与其两端电压成正比：V = IR。欧姆导体的 I–V 特性线为过原点的直线。
Non-ohmic components, such as filament lamps and diodes, do not have a constant resistance. Their I–V graphs are curved. A filament lamp’s resistance increases with temperature, while a diode allows current in only one direction.
非欧姆元件（如灯丝灯泡和二极管）的电阻不是常数，其 I–V 图是曲线。灯丝灯泡的电阻随温度升高而增大，二极管只允许单向导电。
Resistivity experiments often involve measuring resistance of a wire of known length and diameter, then calculating ρ. Temperature coefficients are also testable.
电阻率实验常通过测量已知长度和直径的导线电阻，然后计算 ρ。温度系数也是考点。
5. Series and Parallel Circuits | 串联与并联电路
In a series circuit, current is the same everywhere: I = I₁ = I₂. The total voltage is the sum of individual voltages: Vₜₒₜ = V₁ + V₂. Total resistance: Rₜₒₜ = R₁ + R₂ + …
串联电路中，各处电流相等：I = I₁ = I₂。总电压等于各元件电压之和：Vₜₒₜ = V₁ + V₂。总电阻：Rₜₒₜ = R₁ + R₂ + …
In a parallel circuit, voltage across each branch is the same: V = V₁ = V₂. Total current is the sum of branch currents: Iₜₒₜ = I₁ + I₂. Reciprocal total resistance: 1/Rₜₒₜ = 1/R₁ + 1/R₂.
并联电路中，各支路电压相同：V = V₁ = V₂。总电流等于各支路电流之和：Iₜₒₜ = I₁ + I₂。总电阻的倒数：1/Rₜₒₜ = 1/R₁ + 1/R₂。
These rules are crucial for solving mixed circuits and for calculating power dissipation: P = IV = I²R = V²/R.
这些规则是求解混联电路和计算功率耗散的关键：P = IV = I²R = V²/R。
6. Kirchhoff’s Laws | 基尔霍夫定律
Kirchhoff’s current law (KCL): The sum of currents entering a junction equals the sum leaving it. (Conservation of charge.) Kirchhoff’s voltage law (KVL): The sum of e.m.f.s around a closed loop equals the sum of potential drops. (Conservation of energy.)
基尔霍夫电流定律 (KCL)：流入节点的电流之和等于流出电流之和（电荷守恒）。基尔霍夫电压定律 (KVL)：闭合回路中电动势之和等于电势降落之和（能量守恒）。
These laws are used to analyse multi-loop circuits that cannot be reduced to simple series-parallel arrangements. Setting up loop and node equations is a standard exam task.
这些定律用于分析无法简化为简单串并联的多回路电路。建立回路和节点方程是考试的常规要求。
7. Magnetic Fields and Forces | 磁场与磁力
Magnetic fields are produced by moving charges (currents) and permanent magnets. Field lines point from north to south. The force on a current-carrying conductor in a magnetic field is given by Fleming’s left-hand rule: F = BIL sin θ, where B is the magnetic flux density (tesla, T).
磁场由运动电荷（电流）和永磁体产生。磁感线从北极指向南极。通电导线在磁场中受力由弗莱明左手定则确定：F = BIL sin θ，其中 B 为磁通量密度（特斯拉, T）。
For a charged particle moving in a magnetic field, the force is F = Bqv sin θ. This force is centripetal, causing circular motion. The radius of the path is r = mv / (Bq).
运动电荷在磁场中受力 F = Bqv sin θ。该力充当向心力，产生圆周运动。轨道半径 r = mv / (Bq)。
Magnetic flux Φ = BA cos θ, flux linkage = NΦ. Faraday’s and Lenz’s laws concern changing flux.
磁通量 Φ = BA cos θ，磁链 = NΦ。法拉第定律和楞次定律涉及变化的磁通量。
8. Electromagnetic Induction | 电磁感应
Faraday’s law: The induced e.m.f. in a circuit is directly proportional to the rate of change of magnetic flux linkage. ε = –N ΔΦ / Δt. The negative sign represents Lenz’s law: the induced current opposes the change in flux that produced it.
法拉第定律：回路中的感应电动势与磁链变化率成正比。ε = –N ΔΦ / Δt。负号代表楞次定律：感应电流的方向总是阻碍引起感应的磁通量变化。
This principle is used in generators, microphones, and transformers. A simple a.c. generator has a coil rotating in a magnetic field, producing a sinusoidal e.m.f.
此原理应用于发电机、麦克风和变压器。简单的交流发电机通过线圈在磁场中旋转产生正弦电动势。
Experiments often involve moving a magnet in and out of a coil, observing the induced current direction with a galvanometer.
实验常涉及将磁铁插入和拔出线圈，用检流计观察感应电流的方向。
9. Alternating Current and Transformers | 交流电与变压器
Alternating current (a.c.) varies periodically. Its root mean square (rms) values relate to peak values: Iᵣₘₛ = I₀ / √2, Vᵣₘₛ = V₀ / √2. Power calculation in a.c. uses rms values: P = Iᵣₘₛ Vᵣₘₛ.
交流电周期变化。其方均根值与峰值的关系：Iᵣₘₛ = I₀ / √2，Vᵣₘₛ = V₀ / √2。交流功率计算使用方均根值：P = Iᵣₘₛ Vᵣₘₛ。
A transformer changes voltage levels using two coils wound on a common iron core. For an ideal transformer: Vₚ / Vₛ = Nₚ / Nₛ = Iₛ / Iₚ. Step-up transformers increase voltage, step-down decrease voltage.
变压器利用绕在同一铁芯上的两个线圈改变电压。理想变压器：Vₚ / Vₛ = Nₚ / Nₛ = Iₛ / Iₚ。升压变压器提高电压，降压变压器降低电压。
Efficiency is high, but real transformers have energy losses due to eddy currents, hysteresis, and resistive heating.
变压器效率很高，但实际存在涡流、磁滞和电阻发热等能量损失。
10. Practical Applications and Exam Tips | 实际应用与应试技巧
Key applications include: electric motors (converting electrical to mechanical energy), loudspeakers, relays, generators, transformers, and electromagnetic braking. In IB, power transmission and the advantages of high voltage are often discussed.
关键应用包括：电动机（电能转机械能）、扬声器、继电器、发电机、变压器和电磁制动。IB 中常讨论电力输送及高压输电的优势。
In Edexcel practicals, you should be able to investigate I–V characteristics, measure resistivity, and demonstrate electromagnetic induction. Graphs, units, and significant figures are important.
Edexcel 的实验要求能探究 I–V 特性、测量电阻率并演示电磁感应。图表、单位和有效数字很重要。
Remember to use clear vector diagrams for forces, label directions, and apply the right-hand grip rule for solenoids. Practice past paper questions on circuits with internal resistance of cells.
记住使用清晰的矢量图表示力，标明方向，应用螺线管的右手螺旋定则。练习涉及电池内阻的电路真题。
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