📚 Electricity and Magnetism: Core Principles for IB and Cambridge Physics | 电与磁：IB与剑桥物理核心原理
Electricity and magnetism form the backbone of classical physics, explaining phenomena from static shocks to the generation of alternating current. A deep understanding of electric fields, circuits, magnetic forces, and electromagnetic induction is essential for success in IB and Cambridge Physics. This article covers the key concepts, equations, and real-world applications you need to master.
电与磁构成了经典物理学的支柱，解释了从静电电击到交流电生成的各种现象。深刻理解电场、电路、磁力和电磁感应对于在IB与剑桥物理中取得成功至关重要。本文将涵盖你需要掌握的核心概念、公式和实际应用。
1. Electric Charge and Coulomb's Law | 电荷与库仑定律
charge is the coulomb (C). Charge is quantised: the elementary charge e = 1.60 × 10⁻¹⁹ 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）。电荷是量子化的：基本电荷 e = 1.60 × 10⁻¹⁹ C。
Coulomb's law describes the electrostatic force between two point charges. It is given by F = k |Q₁ Q₂| space ε₀, k = 1/(4πε₀). The force acts along the line joining the centres of the charges.
库仑定律描述了两个点电荷之间的静电力。公式为 F = k |Q₁ Q₂| / r²，其中 k = 8.99 × 10⁹ N m² C⁻² 是库仑常数。用真空介电常数 ε₀ 表示时，k = 1/(4πε₀)。力的方向沿着两电荷中心的连线。
F = k |Q₁ Q₂| / r²
2. Electric Field and Field Lines | 电场与电场线
charge, E = k Q / r², directed away from a positive charge and towards a negative charge.
电场是电荷受到力的区域。电场强度 E 定义为 E = F / q，单位为 N C⁻¹ 或 V m⁻¹。对于点电荷，E = k Q / r²，方向背离正电荷、指向负电荷。
llel plates, E = V / d, where V is the potential difference and d is the plate separation.
电场线用来表示电场：它们从正电荷出发、终止于负电荷，永不相交，其密度表示场强。在匀强电场中，例如两平行板之间，E = V / d，其中 V 为电势差，d 为板间距。
E = F / q, E = k Q / r², E = V / d
3. Electric Potential and Potential Difference | 电势与电势差
charge, V = k Q / r. The potential difference (voltage) between two points is ΔV = W / q.
电场中某点的电势 V 是将单位正电荷从无穷远处移到该点时所做的功。它是一个标量，单位为伏特（V）。对于点电荷，V = k Q / r。两点间的电势差（电压）为 ΔV = W / q。
ial difference of 1 V gains an energy of 1 electronvolt (eV), where 1 eV = 1.60 × 10⁻¹⁹ J.
位于电势 V 处的电荷 q 具有电势能 U = qV。一个电子加速通过 1 V 电势差时获得的能量为 1 电子伏特（eV），1 eV = 1.60 × 10⁻¹⁹ J。
V = k Q / r, U = qV
4. Current, Resistance, and Ohm's Law | 电流、电阻与欧姆定律
conductor is the ratio of voltage across it to current through it: R = V / I, in ohms (Ω).
电流 I 是电荷流动的速率：I = ΔQ / Δt，单位为安培（A）。传统电流方向由正到负。导体的电阻 R 是跨导体电压与通过电流的比值：R = V / I，单位为欧姆（Ω）。
Ohm' = ρ L / A, where ρ is resistivity. Resistivity increases with temperature for most metals.
欧姆定律指出，在恒温条件下，对欧姆导体有 V = IR。电阻取决于几何形状和材料：R = ρ L / A，其中 ρ 为电阻率。大多数金属的电阻率随温度升高而增大。
Electrical power dissipated is P = IV = I² R = V² / R, measured in watts (W).
消耗的电功率为 P = IV = I² R = V² / R，单位为瓦特（W）。
I = ΔQ / Δt, V = IR, R = ρ L / A, P = IV = I² R
5. DC Circuits and Kirchhoff's Laws | 直流电路与基尔霍夫定律
Circuit analysis relies on Kirchhoff's laws. The junction rule (KCL) states that the sum of currents entering a junction equals the sum leaving: ΣIin = ΣIout es that the algebraic sum of potential differences around any closed loop is zero: ΣV = 0.
电路分析依赖基尔霍夫定律。节点电流定律（KCL）指出，流入某节点的电流之和等于流出该节点的电流之和：ΣIin = ΣIout。回路电压定律（KVL）指出，沿任意闭合回路，各段电压的代数和为零：ΣV = 0。
Resistors in series have the same current; total resistance Rtotal R₂ + ... . Resistors in parallel share the same voltage; total resistance is given by 1/Rtotal = 1/R₁ + 1/R₂ + ... . Potential dividers produce a fraction of the input voltage: Vout = Vin × R₂ / (R₁ + R₂).
串联电阻器中的电流相同；总电阻 Rtotal = R₁ + R₂ + ... 。并联电阻器两端的电压相同；总电阻满足 1/Rtotal = 1/R₁ + 1/R₂ + ... 。分压电路可提供输入电压的一部分：Vout = Vin × R₂ / (R₁ + R₂)。
uses the terminal voltage to drop to V = ε − Ir, where ε is the electromotive force (emf).
电池的内阻 r 使端电压降至 V = ε − Ir，其中 ε 为电动势（emf）。
| Series | R = R₁ + R₂ + ... |
| Parallel | 1/R = 1/R₁ + 1/R₂ + ... |
6. Magnetic Fields and the Lorentz Force | 磁场与洛伦兹力
is F = q v B sinθ. This force is always perpendicular to both v and B, so it does no work.
磁场 B 是运动电荷受到力的区域，国际单位为特斯拉（T）。电荷 q 以速度 v 与磁场 B 成 θ 角运动时所受磁力为 F = q v B sinθ。该力始终垂直于 v 和 B，因此不做功。
The direction of the force is given by Fleming' when v is perpendicular to uniform B. The period T = 2π m / (q B) is independent of speed.
力的方向由左手定则（传统电流方向）或右手定则（正电荷）确定。当 v 垂直于匀强磁场 B 时，带电粒子做圆周运动，半径 r = m v / (q B)。周期 T = 2π m / (q B) 与速度无关。
F = q v B sinθ, r = m v / (q B), T = 2π m / (q B)
7. Magnetic Force on Current-Carrying Conductors | 载流导体所受磁力
rection is again given by the left-hand rule, where the current replaces the motion of positive charge.
位于磁场中的载流导体会受到作用力。对于长度为 L、电流为 I 且与磁场 B 成 θ 角的直导线，F = B I L sinθ。方向同样可用左手定则确定，此时电流代替了正电荷的运动方向。
nd θ the angle between the field and the normal to the coil. This principle is used in moving-coil galvanometers and electric motors.
对于匀强磁场中匝数为 N 的矩形线圈，力矩为 τ = N I A B sinθ，其中 A 为线圈面积，θ 为磁场与线圈法线的夹角。这一原理广泛应用于动圈式电流计和电动机。
F = B I L sinθ, τ = N I A B sinθ
8. Electromagnetic Induction: Faraday's and Lenz's Laws | 电磁感应：法拉第与楞次定律
cosθ, where θ is the angle between B and the normal to the loop. The unit is the weber (Wb). Flux linkage is NΦ.
穿过回路的磁通量 Φ 为 Φ = B A cosθ，其中 θ 是 B 与回路法线的夹角，单位为韦伯（Wb）。磁链为 NΦ。
Faraday' the induced emf ε equals the negative rate of change of flux linkage: ε = −N ΔΦ / Δt. Lenz' ves the direction: the induced current always opposes the change in flux that produced it.
法拉第定律指出，感应电动势 ε 等于磁链变化率的负值：ε = −N ΔΦ / Δt。楞次定律给出了方向：感应电流总是反抗引起它的磁通量变化。
o B, the motional emf is ε = B L v. Induction is the basis of generators and transformers.
当长度为 L 的直导线以速度 v 垂直于磁场 B 运动时，动生电动势为 ε = B L v。电磁感应是发电机和变压器的基础。
Φ = B A cosθ, ε = −N ΔΦ / Δt, ε = B L v
9. Alternating Current and Transformers | 交流电与变压器
f is the angular frequency. The root-mean-square (rms) values relate to the peak values: Vrms = V₀ / √2, Irms = I₀ / √2. Domestic mains supply typically has Vrms = 230 V at 50 Hz.
交流电（AC）按正弦规律变化。瞬时电压为 v = V₀ sin(ω t)，其中 V₀ 为峰值电压，ω = 2π f 为角频率。方均根（rms）值与峰值的关系为：Vrms = V₀ / √2，Irms = I₀ / √2。家用市电通常为 Vrms = 230 V、50 Hz。
An ideal transformer changes voltage levels without power loss. The turns ratio determines the voltage ratio: Vs / Vp = Ns / Np. For 100% efficiency, Pp = Ps, so Ip Vp = Is Vs. Step-up transformers increase voltage and decrease current; step-down transformers do the opposite.
理想变压器无功率损耗地改变电压。匝数比决定电压比：Vs / Vp = Ns / Np。效率为 100% 时，Pp = Ps，因此 Ip Vp = Is Vs。升压变压器升高电压、降低电流；降压变压器则相反。
Vrms = V₀ / √2, Vs / Vp = Ns / Np
10. Capacitance and RC Circuits | 电容与RC电路
tor, C = ε₀ A / d in vacuum. With a dielectric of relative permittivity κ, C = κ ε₀ A / d.
电容器储存电荷与能量。电容 C = Q / V，单位为法拉（F）。对于真空平行板电容器，C = ε₀ A / d。加相对介电常数为 κ 的电介质后，C = κ ε₀ A / d。
ed in a capacitor is U = ½ C V² = ½ Q V = ½ Q² / C. Capacitors in parallel add directly: Ceq = C₁ + C₂ + ... . Capacitors in series combine as 1/Ceq = 1/C₁ + 1/C₂ + ... .
电容器储存的能量为 U = ½ C V² = ½ Q V = ½ Q² / C。并联电容直接相加：Ceq = C₁ + C₂ + ... 。串联电容的组合公式为 1/Ceq = 1/C₁ + 1/C₂ + ... 。
). During discharging, q = Q₀ exp(−t / τ). The time constant is the time to reach about 63% of the final value.
在RC电路中，充放电过程按指数曲线进行，时间常数 τ = R C。充电时，q = Q₀ (1 − exp(−t / τ))，V = V₀ (1 − exp(−t / τ))。放电时，q = Q₀ exp(−t / τ)。时间常数是达到最终值约 63% 所需的时间。
C = Q / V, C = ε₀ A / d, U = ½ C V², τ = R C
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