📚 Year 13 CIE Physics: Core Content Review | Year 13 CIE 物理：核心知识点梳理
Year 13 CIE A Level Physics (9702) builds on the AS foundation and deepens understanding of fields, waves, thermal physics, and modern physics. The core A2 topics range from circular motion and gravitational fields to quantum and nuclear phenomena, equipping students with analytical tools and conceptual clarity for the final examinations.
Year 13 CIE A Level 物理 (9702) 在 AS 基础之上深入探讨场、波、热力学和近代物理。核心 A2 主题涵盖圆周运动、引力场、量子现象与核物理等内容，帮助考生建立分析工具和清晰概念，以应对最终的考试。
1. Circular Motion | 圆周运动
Angular displacement is measured in radians. Angular velocity ω is the rate of change of angle: ω = Δθ / Δt.
角位移以弧度为单位。角速度 ω 是角度的变化率：ω = Δθ / Δt。
Linear speed v is related to angular velocity by v = ωr, where r is the radius of the circular path.
线速度 v 与角速度的关系为 v = ωr，其中 r 为圆周半径。
Centripetal acceleration a = v² / r = ω²r, always directed towards the centre of the circle.
向心加速度 a = v² / r = ω²r，始终指向圆心。
Centripetal force F = mv² / r = mω²r is not a new force but a resultant force provided by tension, gravity, friction, etc.
向心力 F = mv² / r = mω²r 并非新的力，而是由张力、重力、摩擦力等提供的合力。
2. Gravitational Fields | 引力场
Newton’s law of gravitation: F = G m₁ m₂ / r², where G is the universal gravitational constant.
牛顿万有引力定律：F = G m₁ m₂ / r²，其中 G 为引力常数。
Gravitational field strength g is force per unit mass: g = F / m. For a point mass, g = GM / r².
引力场强度 g 是单位质量所受的力：g = F / m。对于质点，g = GM / r²。
Gravitational potential φ = –GM / r (setting zero at infinity). Work done in moving a mass m is ΔW = m Δφ.
引力势 φ = –GM / r（无穷远处为零）。移动质量 m 所需做功为 ΔW = m Δφ。
Satellite motion: for a circular orbit, gravitational force provides centripetal force, yielding orbital period T² ∝ r³.
卫星运动：对于圆形轨道，引力提供向心力，从而得出轨道周期 T² ∝ r³（开普勒第三定律）。
3. Simple Harmonic Motion | 简谐运动
SHM is an oscillation where acceleration a is directly proportional to displacement x from equilibrium and always directed towards it: a = –ω²x.
简谐运动中加速度 a 与位移 x 成正比且方向相反：a = –ω²x。
Displacement can be written as x = x₀ sin(ωt) or x = x₀ cos(ωt), where x₀ is amplitude and ω = 2πf.
位移可写作 x = x₀ sin(ωt) 或 x = x₀ cos(ωt)，其中 x₀ 为振幅，ω = 2πf。
Velocity v = ±ω √(x₀² – x²) and maximum speed v_max = ωx₀. Total energy E = ½ m ω² x₀², alternating between kinetic and potential forms.
速度 v = ±ω √(x₀² – x²)，最大速率 v_max = ωx₀。总能量 E = ½ m ω² x₀²，在动能和势能之间交替转换。
Free oscillations, damping (light, critical, heavy), and forced oscillations with resonance at driving frequency f = natural frequency f₀ are key phenomena.
自由振荡、阻尼（弱阻尼、临界阻尼、过阻尼）以及强迫振荡在驱动频率 f 等于固有频率 f₀ 时发生共振，这是关键现象。
4. Thermal Physics | 热力学
Temperature is related to the average kinetic energy of particles. The ideal gas equation is pV = nRT = NkT, where n is moles and N is number of molecules.
温度与粒子平均动能相关。理想气体状态方程为 pV = nRT = NkT，其中 n 为摩尔数，N 为分子数。
Kinetic theory gives pV = ⅓ N m
分子动理论给出 pV = ⅓ N m
Internal energy U is the sum of kinetic and potential energies of particles. The first law of thermodynamics: ΔU = Q + W (work done on the system).
内能 U 是粒子动能与势能的总和。热力学第一定律：ΔU = Q + W（W 为对系统做功）。
Key processes: isothermal (ΔU=0, Q = –W), adiabatic (Q=0, ΔU = W), isochoric (W=0, ΔU = Q), and isobaric. Work done W = –p ΔV.
关键过程：等温过程 (ΔU=0, Q = –W)，绝热过程 (Q=0, ΔU = W)，等容过程 (W=0, ΔU = Q) 和等压过程。做功 W = –p ΔV。
5. Electric Fields | 电场
Coulomb’s law: force between two point charges F = k Q₁ Q₂ / r², where k = 1/(4πε₀). Electric field strength E = F / q.
库仑定律：两点电荷间作用力 F = k Q₁ Q₂ / r²，其中 k = 1/(4πε₀)。电场强度 E = F / q。
For a point charge, E = kQ / r² and electric potential V = kQ / r (zero at infinity). The potential difference ΔV = ΔW / q.
对点电荷，E = kQ / r²，电势 V = kQ / r（无穷远处为零）。电势差 ΔV = ΔW / q。
In a uniform field, E = V / d. The path of a charged particle moving through an electric field follows a parabolic trajectory.
在匀强电场中，E = V / d。带电粒子在电场中运动轨迹呈抛物线。
6. Capacitance | 电容
Capacitance C = Q / V; unit: farad (F). For a parallel-plate capacitor, C = ε₀ A / d, where A is plate area and d is separation.
电容 C = Q / V，单位为法拉 (F)。平行板电容器的电容 C = ε₀ A / d，A 为板面积，d 为板间距。
Inserting a dielectric of relative permittivity εᵣ increases capacitance: C = εᵣ ε₀ A / d.
插入相对介电常数为 εᵣ 的介质能增大电容：C = εᵣ ε₀ A / d。
Energy stored in a capacitor: U = ½ QV = ½ CV² = ½ Q² / C.
电容器储存的能量：U = ½ QV = ½ CV² = ½ Q² / C。
Charging and discharging through a resistor follow exponential laws; time constant τ = RC.
通过电阻的充放电遵循指数规律，时间常数 τ = RC。
7. Magnetic Fields | 磁场
Force on a moving charge: F = B q v sinθ, with direction given by Fleming’s left-hand rule.
运动电荷所受洛伦兹力：F = B q v sinθ，方向由左手定则判断。
Force on a current-carrying conductor: F = B I L sin θ. The torque on a coil in a magnetic field is used in electric motors.
载流导线所受安培力：F = B I L sinθ。通电线圈在磁场中所受的力矩被用于电动机。
Magnetic flux density B near a long straight wire: B = μ₀ I / (2π r), and inside a solenoid: B = μ₀ n I.
长直导线周围的磁通密度 B = μ₀ I / (2π r)，螺线管内部 B = μ₀ n I。
The Hall effect arises when a magnetic field exerts a force on charge carriers in a conductor, setting up a transverse Hall voltage V_H = B I / (n q t).
霍尔效应是磁场对导体中载流子施加力，从而建立横向霍尔电压 V_H = B I / (n q t)。
8. Electromagnetic Induction | 电磁感应
Magnetic flux Φ = B A cosθ. Faraday’s law: induced emf ε = – dΦ / dt. Lenz’s law gives the direction of induced current to oppose the change in flux.
磁通量 Φ = B A cosθ。法拉第定律：感应电动势 ε = – dΦ / dt。楞次定律确定感应电流方向——总是阻碍磁通量的变化。
For a conductor moving perpendicular to a uniform field, ε = B L v.
对于垂直于匀强磁场运动的导体，ε = B L v。
An AC generator produces a sinusoidal emf. A transformer uses mutual induction to step voltages up or down, with V_s / V_p = N_s / N_p for an ideal transformer.
交流发电机产生正弦电动势。变压器利用互感实现电压的升降，理想变压器满足 V_s / V_p = N_s / N_p。
9. Alternating Currents | 交流电
Root-mean-square values: V_rms = V₀ / √2, I_rms = I₀ / √2. Average power P = I_rms V_rms = ½ I₀ V₀ for resistive loads.
均方根值：V_rms = V₀ / √2，I_rms = I₀ / √2。纯电阻负载的平均功率 P = I_rms V_rms = ½ I₀ V₀。
Reactances: capacitive reactance X_C = 1 / (ωC), inductive reactance X_L = ωL. Impedance Z combines resistance and reactance, leading to phase differences between voltage and current.
电抗：容抗 X_C = 1 / (ωC)，感抗 X_L = ωL。阻抗 Z 综合了电阻与电抗，使得电压与电流之间出现相位差。
Resonance in an LCR circuit occurs when X_C = X_L, giving a maximum current and a resonant frequency f₀ = 1 / (2π √(LC)).
LCR 电路谐振发生在 X_C = X_L 时，电流达到最大，谐振频率 f₀ = 1 / (2π √(LC))。
Rectification (half-wave and full-wave) converts AC to DC; smoothing using a capacitor reduces ripple.
整流（半波和全波）将交流变为直流；利用电容进行滤波以减小纹波。
10. Quantum Physics | 量子物理
Photon energy E = hf = hc / λ. The photoelectric effect gives hf = Φ + KE_max, where Φ is the work function.
光子能量 E = hf = hc / λ。光电效应方程 hf = Φ + KE_max，其中 Φ 为逸出功。
Wave–particle duality: particles have a de Broglie wavelength λ = h / p, where p is momentum. Electron diffraction confirms wave nature.
波粒二象性：粒子具有德布罗意波长 λ = h / p，p 为动量。电子衍射证实了波动性。
Atomic line spectra arise from electron transitions between discrete energy levels; ΔE = hf = E₂ – E₁.
原子线状光谱来源于电子在分立能级间的跃迁；ΔE = hf = E₂ – E₁。
Emission and absorption spectra provide evidence for quantized energy states, consistent with the Bohr model.
发射光谱和吸收光谱为量子化能态提供了证据，与玻尔模型一致。
11. Nuclear Physics | 核物理
Mass defect Δm is the difference between the mass of a nucleus and the sum of its constituent nucleons. Binding energy E_b = Δm c².
质量亏损 Δm 是原子核质量与其组成核子质量之和的差。结合能 E_b = Δm c²。
Radioactive decay: alpha (⁴₂He), beta-minus (electron), beta-plus (positron), and gamma (photon). Decay law: N = N₀ e^(-λt).
放射性衰变：α 衰变 (⁴₂He)，β⁻ 衰变 (电子)，β⁺ 衰变 (正电子) 和 γ 衰变 (光子)。衰变规律：N = N₀ e^(-λt)。
Half-life T_½ = ln2 / λ. Activity A = λN. Carbon dating and medical tracers utilise decay principles.
半衰期 T_½ = ln2 / λ。活度 A = λN。碳年代测定和医用示踪剂均应用了衰变原理。
| Decay Type | Particle | Change in A | Change in Z |
|---|---|---|---|
| Alpha | ⁴₂He | –4 | –2 |
| Beta-minus | e⁻ (electron) | 0 | +1 |
| Beta-plus | e⁺ (positron) | 0 | –1 |
| Gamma | Photon | 0 | 0 |
Nuclear fission splits a heavy nucleus into two lighter ones, releasing energy. Nuclear fusion combines light nuclei, powering stars.
核裂变将重核分裂为两个较轻的核并释放能量。核聚变将轻核结合，为恒星提供能量。
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