📚 Core Topics Overview for CAIE A2 Physics | CAIE A2 物理核心知识点梳理
In Year 13 CAIE Physics, students deepen their understanding through advanced mechanics, fields, oscillations, thermodynamics, electromagnetism, and modern physics. This article provides a concise yet comprehensive review of the essential concepts, ensuring you can navigate the A2 syllabus with confidence.
在十三年级 CAIE 物理课程中，学生将借助进阶力学、场论、振动、热力学、电磁学和近代物理等专题深化理解。本文对这些核心知识点进行简明而全面的梳理，帮助你有把握地掌握 A2 考试大纲。
1. Circular Motion | 圆周运动
An object moving in a circle of radius r at constant speed v experiences a centripetal acceleration a = v² / r directed towards the centre. The angular velocity ω = v / r = 2πf , where f is frequency, so the acceleration can also be written as a = ω² r.
物体以恒定速率 v 在半径为 r 的圆周上运动时，受到指向圆心的向心加速度 a = v² / r。角速度 ω = v / r = 2πf（f 为频率），因此加速度也可写作 a = ω² r。
Centripetal force F = mv² / r = mω² r is the net force towards the centre, required to maintain circular motion. It is not a separate force but a resultant of physical forces such as tension, gravity, or friction.
向心力 F = mv² / r = mω² r 是维持圆周运动所需的指向圆心的合力。它不是某种单独的力，而是张力、重力或摩擦力等实际力的合力。
In vertical circular motion, the tension or normal reaction varies with position; at the top, minimum speed is √(gr) for an object to stay on the track.
在竖直面内的圆周运动中，绳的张力或轨道支持力随位置变化；在最高点，物体不落下的最小速率为 √(gr)。
2. Gravitational Fields | 引力场
Newton’s law of gravitation states that the force between two point masses M and m separated by distance r is F = GMm / r², where G is the gravitational constant. The gravitational field strength g at a point is the force per unit mass: g = F / m = GM / r².
牛顿万有引力定律指出，两个质点 M 与 m 相距 r 时的引力为 F = GMm / r²，其中 G 为引力常量。引力场强度 g 定义为单位质量所受的力：g = F / m = GM / r²。
For a spherical mass, the field outside is identical to that of a point mass at the centre. Gravitational potential V = –GM / r is the work done per unit mass to bring a small mass from infinity to that point; field strength is the negative gradient of potential: g = –dV / dr.
对于球对称质量，外部的场等同于所有质量集中在球心的质点。引力势 V = –GM / r 表示将单位质量从无穷远移至该点外力所做的功；场强为势的负梯度：g = –dV / dr。
Satellites orbit the Earth in stable paths when centripetal force equals gravitational force: GMm / r² = mv² / r, leading to orbital speed v = √(GM / r) and period T² ∝ r³ (Kepler’s third law).
当向心力等于引力时，人造卫星可沿稳定轨道运行：GMm / r² = mv² / r，由此得到轨道速率 v = √(GM / r) 以及周期 T² ∝ r³（开普勒第三定律）。
3. Simple Harmonic Motion | 简谐运动
Simple harmonic motion (SHM) occurs when the restoring force is proportional to displacement from equilibrium and directed opposite to it: F = –kx. This leads to an acceleration a = –ω² x, where ω is angular frequency.
当回复力与质点偏离平衡位置的位移成正比且方向相反时，物体做简谐运动（F = –kx）。由此得到加速度 a = –ω² x，ω 为角频率。
The solutions for displacement, velocity and acceleration are x = x₀ sin(ωt) or x = x₀ cos(ωt), v = ωx₀ cos(ωt), a = –ω² x₀ sin(ωt). Maximum speed vₘₐₓ = ωx₀ and maximum acceleration aₘₐₓ = ω² x₀.
位移、速度和加速度的解为 x = x₀ sin(ωt) 或 x = x₀ cos(ωt)，v = ωx₀ cos(ωt)，a = –ω² x₀ sin(ωt)。最大速率 vₘₐₓ = ωx₀，最大加速度 aₘₐₓ = ω² x₀。
Period of a mass‐spring system: T = 2π√(m / k); period of a simple pendulum for small amplitudes: T = 2π√(L / g). Energy in SHM continuously exchanges between kinetic and potential, total energy E = ½ m ω² x₀².
弹簧振子的周期 T = 2π√(m / k)；小振幅单摆的周期 T = 2π√(L / g)。简谐运动中的能量在动能与势能之间不断转化，总能量 E = ½ m ω² x₀²。
4. Thermal Physics and Ideal Gases | 热力学与理想气体
The kinetic theory of gases relates macroscopic quantities to microscopic motion: pressure p = ⅓ (N / V) m ⟨c²⟩, where N/V is number density, m is molecular mass, and ⟨c²⟩ is the mean square speed. Hence the average translational kinetic energy of a molecule is ½ m ⟨c²⟩ = (3/2) kT.
气体动理论将宏观量与微观运动联系起来：压强 p = ⅓ (N / V) m ⟨c²⟩，其中 N/V 为数密度，m 为分子质量，⟨c²⟩ 为方均速率。因此分子的平均平动动能 ½ m ⟨c²⟩ = (3/2) kT。
The ideal gas equation is pV = nRT = NkT, where n is number of moles, R is molar gas constant, N is number of molecules, and k is Boltzmann constant. Real gases deviate at high pressure and low temperature.
理想气体状态方程为 pV = nRT = NkT，n 为摩尔数，R 为摩尔气体常量，N 为分子数，k 为玻尔兹曼常量。真实气体在高压低温下会产生偏离。
The first law of thermodynamics is ΔU = Q + W, with sign conventions: Q positive when heat is added to the system, W positive when work is done on the system. Isothermal, adiabatic, isochoric and isobaric processes each impose specific constraints.
热力学第一定律 ΔU = Q + W，符号规定：系统吸热 Q 为正，外界对系统做功 W 为正。等温、绝热、等容和等压过程各自有不同的约束条件。
5. Electric Fields | 电场
Coulomb’s law gives the force between two point charges Q and q: F = (1 / 4πε₀) Q q / r². Electric field strength E is defined as force per unit positive charge: E = F / q. For a point charge, E = (1 / 4πε₀) Q / r².
库仑定律描述两点电荷 Q 与 q 之间的作用力：F = (1 / 4πε₀) Q q / r²。电场强度 E 定义为单位正电荷所受的力：E = F / q。对于点电荷，E = (1 / 4πε₀) Q / r²。
Electric potential V at a point is the work done per unit charge in bringing a small positive test charge from infinity to that point: V = (1 / 4πε₀) Q / r. The field strength is the negative potential gradient: E = –dV / dr. Equipotential surfaces are perpendicular to field lines.
电场中某点的电势 V 等于将单位正试探电荷从无穷远移至该点外力所做的功：V = (1 / 4πε₀) Q / r。场强是电势的负梯度：E = –dV / dr。等势面处处与电场线垂直。
In a uniform electric field between parallel plates, E = V / d, and the force on a charge is F = qE. Motion of charged particles can be analysed using kinematic equations.
在平行板间的匀强电场中，E = V / d，电荷所受电场力 F = qE。带电粒子在电场中的运动可借助运动学方程进行分析。
6. Capacitance | 电容
Capacitance C is defined as charge stored per unit potential difference: C = Q / V. For a parallel plate capacitor, C = ε₀ εᵣ A / d, where εᵣ is relative permittivity, A is plate area and d is separation.
电容 C 定义为电容器储存的电荷与两端电势差的比值：C = Q / V。平行板电容器的电容 C = ε₀ εᵣ A / d，其中 εᵣ 为相对介电常数，A 为极板面积，d 为间距。
Energy stored in a capacitor is given by W = ½ Q V = ½ C V² = ½ Q² / C. This energy resides in the electric field between the plates.
电容器储存的能量为 W = ½ Q V = ½ C V² = ½ Q² / C。这些能量储存在两极板之间的电场中。
Capacitors charge and discharge through a resistor with an exponential time dependence: Q = Q₀ e^(–t / RC), V = V₀ e^(–t / RC), where the time constant τ = RC. After one time constant the charge falls to about 37% of its initial value.
电容器通过电阻进行充放电时，电荷和电压按指数规律变化：Q = Q₀ e^(–t / RC)，V = V₀ e^(–t / RC)，时间常数 τ = RC。经过一个时间常数，电荷降至初始值的大约 37%。
7. Magnetic Fields | 磁场
A current-carrying conductor placed in a magnetic field experiences a force: F = B I l sinθ, where B is magnetic flux density, I is current, l is conductor length, and θ is the angle between current and field. Fleming’s left-hand rule gives the direction of force.
通电导线在磁场中受到安培力：F = B I l sinθ，其中 B 为磁通量密度，I 为电流，l 为导线长度，θ 为电流与磁场方向的夹角。左手定则可判断力的方向。
A moving charge in a magnetic field experiences the Lorentz force F = B q v sinθ. If the velocity is perpendicular to the field, the charge follows a circular path with radius r = mv / (Bq). The period is independent of speed: T = 2πm / (Bq).
运动电荷在磁场中受到洛伦兹力 F = B q v sinθ。若速度与磁场垂直，电荷将做圆周运动，半径 r = mv / (Bq)。周期与速率无关：T = 2πm / (Bq)。
Magnetic flux φ = B A cosθ, where θ is the angle between the field and the normal to area A. Flux density is measured in tesla (T). The Hall effect can be used to determine the type and density of charge carriers.
磁通量 φ = B A cosθ，θ 为磁场与面积法线方向的夹角。磁通量密度的单位为特斯拉（T）。霍尔效应可用来测定载流子的类型和浓度。
8. Electromagnetic Induction | 电磁感应
Faraday’s law states that the induced e.m.f. in a circuit is equal to the rate of change of magnetic flux linkage: ε = –d(Nφ) / dt. The negative sign indicates Lenz’s law — induced current opposes the change in flux.
法拉第电磁感应定律：回路中的感应电动势等于磁链的变化率 ε = –d(Nφ) / dt。负号体现了楞次定律——感应电流的磁场总是阻碍磁通量的变化。
For a conductor moving perpendicularly through a magnetic field, the induced e.m.f. across its ends is ε = B l v. In a rotating coil, ε = B A N ω sin(ωt), which forms the basis of the a.c. generator.
对于垂直切割磁感线的导线，两端感应电动势 ε = B l v。在旋转线圈中，ε = B A N ω sin(ωt)，这是交流发电机的基本原理。
Transformers rely on mutual induction: Vₛ / Vₚ = Nₛ / Nₚ. For an ideal transformer, power input equals power output, Iₚ Vₚ = Iₛ Vₛ. Eddy currents in cores are reduced by lamination.
变压器基于互感原理：Vₛ / Vₚ = Nₛ / Nₚ。对于理想变压器，输入功率等于输出功率，Iₚ Vₚ = Iₛ Vₛ。铁芯中的涡流通过叠片结构予以减小。
9. Alternating Currents | 交流电
An alternating voltage can be described as V = V₀ sin(ωt). The root-mean-square (r.m.s.) value is Vᵣₘₛ = V₀ / √2, and similarly Iᵣₘₛ = I₀ / √2. These r.m.s. values are used to calculate average power: Pₐᵥ = Iᵣₘₛ Vᵣₘₛ = Iᵣₘₛ² R.
交流电压可表示为 V = V₀ sin(ωt)。均方根值为 Vᵣₘₛ = V₀ / √2，类似地 Iᵣₘₛ = I₀ / √2。计算平均功率时使用均方根值：Pₐᵥ = Iᵣₘₛ Vᵣₘₛ = Iᵣₘₛ² R。
In a purely resistive circuit, voltage and current are in phase. In a purely inductive circuit, current lags voltage by 90°; in a pure capacitor, current leads voltage by 90°. Reactance for inductance is X_L = ωL, for capacitance X_C = 1/(ωC).
在纯电阻电路中，电压与电流同相。纯电感电路中电流落后电压 90°；纯电容电路中电流超前电压 90°。感抗 X_L = ωL，容抗 X_C = 1/(ωC)。
Impedance Z of an LCR series circuit is Z = √(R² + (X_L − X_C)²). Resonance occurs when X_L = X_C, giving Zₘᵢₙ = R and maximum current, with resonant frequency f₀ = 1 / (2π√(LC)).
LCR 串联电路的阻抗 Z = √(R² + (X_L − X_C)²)。当 X_L = X_C 时发生谐振，此时阻抗最小 Zₘᵢₙ = R，电流最大，谐振频率 f₀ = 1 / (2π√(LC))。
10. Quantum Physics | 量子物理
Photoelectric effect experiments show that electrons are emitted from a metal surface only when the incident light frequency exceeds a threshold frequency f₀. The maximum kinetic energy of photoelectrons is Kₘₐₓ = hf − φ, where h is Planck’s constant and φ is the work function.
光电效应实验表明，只有当入射光频率超过某一截止频率 f₀ 时，金属表面才会逸出电子。光电子的最大动能 Kₘₐₓ = hf − φ，其中 h 为普朗克常量，φ 为逸出功。
Light behaves as both a wave and a stream of photons, each carrying energy E = hf and momentum p = h / λ. The de Broglie wavelength of a particle is λ = h / p, which is observable for microscopic particles such as electrons.
光既表现出波动性，又可看作光子流，每个光子携带能量 E = hf 和动量 p = h / λ。粒子的德布罗意波长 λ = h / p，这在电子等微观粒子身上可被观察到。
Emission and absorption spectra demonstrate discrete energy levels in atoms. When an electron transitions between levels, a photon of energy ΔE = hf is emitted or absorbed. The wave function encodes probability, and the Heisenberg uncertainty principle implies ΔxΔp ≥ h / 4π.
发射与吸收光谱证明了原子中存在分立的能级。电子在两能级间跃迁时，会发射或吸收能量为 ΔE = hf 的光子。波函数包含概率信息，海森伯不确定性原理表明 ΔxΔp ≥ h / 4π。
11. Nuclear and Particle Physics | 核与粒子物理
Nuclear stability depends on the neutron-to-proton ratio. The strong nuclear force overcomes electrostatic repulsion between protons. Radioactive decay follows the exponential law N = N₀ e^(−λt), with half-life T½ = ln2 / λ and decay constant λ.
原子核的稳定性取决于中子–质子比。强核力克服了质子间的静电排斥。放射性衰变遵循指数规律 N = N₀ e^(−λt)，半衰期 T½ = ln2 / λ，λ 为衰变常量。
Alpha decay reduces mass number by 4 and atomic number by 2; beta⁻ decay converts a neutron to a proton, emitting an electron and an antineutrino; gamma decay releases excess energy without changing nucleon composition.
α 衰变使质量数减少 4、原子序数减少 2；β⁻ 衰变中中子转变为质子，放出电子和反中微子；γ 衰变释放多余能量而不改变核子组成。
Quarks combine to form hadrons: protons (uud) and neutrons (udd). The Standard Model also includes leptons and gauge bosons. Nuclear reactions conserve charge, baryon number, lepton number, mass–energy and momentum.
夸克组合成强子：质子 (uud)、中子 (udd)。标准模型还包含轻子和规范玻色子。核反应遵守电荷、重子数、轻子数、质能以及动量的守恒。
Fission splits a heavy nucleus into lighter fragments with release of energy; fusion combines light nuclei at very high temperature, also releasing energy. Mass defect Δm is related to binding energy by E = Δm c².
裂变使重核分裂为较轻的碎片并释放能量；聚变在极高温度下使轻核结合，同样释放能量。质量亏损 Δm 与结合能的关系为 E = Δm c²。
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