📚 Year 13 CIE Physics: Core Concepts Overview | Year 13 CIE 物理：核心知识点梳理
Welcome to this comprehensive revision guide covering the essential topics in Year 13 CIE Physics. In this article, we will systematically review key concepts, formulas, and applications that frequently appear in the A2 examinations. Mastering these areas is crucial for achieving a top grade.
欢迎阅读这份全面复习指南，涵盖 Year 13 CIE 物理的核心课题。本文系统梳理了 A2 考试中常见的关键概念、公式及应用，掌握这些领域对于取得优异成绩至关重要。
1. Circular Motion | 圆周运动
An object moving in a circle at constant speed undergoes uniform circular motion. Its angular velocity ω is defined as the rate of change of angular displacement: ω = Δθ/Δt = 2πf = 2π/T, where T is the period. The linear speed v is related to ω by v = rω.
以恒定速率做圆周运动的物体进行匀速圆周运动。其角速度 ω 定义为角位移的变化率：ω = Δθ/Δt = 2πf = 2π/T，其中 T 为周期。线速率 v 与 ω 的关系为 v = rω。
The centripetal acceleration a always points toward the centre, with magnitude:
a = v² / r = r ω²
向心加速度 a 始终指向圆心，大小为 a = v²/r = rω²。
The centripetal force F required to maintain circular motion is F = m a = m v²/r = m r ω². This force is provided by tension, gravity, friction, or electromagnetic forces depending on the context.
维持圆周运动所需的向心力 F 为 F = m a = m v²/r = m r ω²。该力可由拉力、重力、摩擦力或电磁力提供，具体取决于情境。
2. Gravitational Fields | 引力场
Newton’s law of gravitation states that the force between two point masses is F = G M m / 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，两个点质量之间的引力为 F = G M m / r²，G 为引力常量。某点的引力场强度 g 为单位质量所受的力：g = F/m = GM/r²。
For a uniform spherical mass, the field outside the sphere is identical to that of a point mass at its centre. The field strength decreases with the square of the distance.
对于均匀球体，球外部的引力场与位于球心的点质量产生的场完全相同。场强随距离的平方反比衰减。
The gravitational potential V at a point is work done per unit mass in bringing a test mass from infinity to that point: V = –GM/r. The potential energy of a mass m is U = m V. Equipotential surfaces are perpendicular to field lines.
引力势 V 是将单位质量从无穷远移至该点所做的功：V = –GM/r。质量 m 的势能为 U = m V。等势面与场线处处垂直。
3. Simple Harmonic Motion | 简谐运动
Simple harmonic motion (SHM) occurs when the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction. The defining equation is a = – ω² x, where x is displacement and ω is the angular frequency.
简谐运动发生在回复力与离开平衡位置的位移成正比且方向相反时。其定义方程为 a = – ω² x，x 为位移，ω 为角频率。
Key quantities for a simple pendulum or mass‑spring system: period T = 2π/ω. For a mass‑spring system, T = 2π √(m/k); for a simple pendulum with small amplitude, T = 2π √(l/g).
单摆或弹簧振子的关键量：周期 T = 2π/ω。弹簧振子 T = 2π √(m/k)；小角度单摆 T = 2π √(l/g)。
The velocity and acceleration as functions of time are v = – ω x₀ sin(ωt) and a = – ω² x₀ cos(ωt), where x₀ is the amplitude. Energy continually interchanges between kinetic and potential forms, but the total energy remains constant: E = ½ m ω² x₀².
速度和加速度随时间的变化为 v = – ω x₀ sin(ωt) 和 a = – ω² x₀ cos(ωt)，其中 x₀ 为振幅。能量在动能与势能之间不断转换，但总能量守恒：E = ½ m ω² x₀²。
4. Thermal Physics and Ideal Gases | 热物理与理想气体
The ideal‑gas equation is pV = nRT, where n is the number of moles and R is the molar gas constant. It can also be expressed in terms of the Boltzmann constant k as pV = N k T, where N is the number of molecules.
理想气体状态方程为 pV = nRT，n 为物质的量，R 为摩尔气体常量。也可用玻尔兹曼常量 k 表示为 pV = N k T，N 为分子数。
The kinetic theory links macroscopic pressure to microscopic motion: p = ⅓ ρ ⟨c²⟩, where ρ is density and ⟨c²⟩ is the mean square speed. The average translational kinetic energy of a molecule is ½ m ⟨c²⟩ = (3/2) k T.
分子动理论将宏观压强与微观运动联系起来：p = ⅓ ρ ⟨c²⟩，ρ 为密度，⟨c²⟩ 为方均速率。分子的平均平移动能为 ½ m ⟨c²⟩ = (3/2) k T。
The first law of thermodynamics is ΔU = Q + W, where ΔU is the change in internal energy, Q is heat supplied to the system, and W is work done on the system. For an ideal gas, internal energy depends only on temperature.
热力学第一定律为 ΔU = Q + W，ΔU 为内能变化，Q 为系统吸收的热量，W 为对系统做的功。对于理想气体，内能仅取决于温度。
5. Electric Fields | 电场
Coulomb’s law gives the force between two point charges: F = k Q q / r², where k = 1/(4π ε₀). Electric field strength E is force per unit positive charge: E = F/q. For a point charge, E = k Q / r².
库仑定律描述两点电荷间的力：F = k Q q / r²，k = 1/(4π ε₀)。电场强度 E 为单位正电荷所受的力：E = F/q。点电荷的电场强度 E = k Q / r²。
Electric potential V due to a point charge is V = k Q / r. The potential energy of a charge q in a potential V is U = q V. Equipotential surfaces are perpendicular to electric field lines.
点电荷产生的电势 V = k Q / r。电荷 q 在电势 V 中的电势能为 U = q V。等势面与电场线垂直。
In a uniform electric field between parallel plates, E = V/d, and the force on a charge is F = q E. An electron accelerated through a potential difference ΔV gains kinetic energy e ΔV.
在平行板间的匀强电场中，E = V/d，电荷受力 F = q E。电子经电势差 ΔV 加速后获得动能 e ΔV。
6. Capacitance | 电容
Capacitance C is defined as charge stored per unit potential difference: C = Q/V. The energy stored in a capacitor is W = ½ Q V = ½ C V² = ½ Q²/C.
电容 C 定义为储存电荷与电势差之比：C = Q/V。电容器储存的能量为 W = ½ Q V = ½ C V² = ½ Q²/C。
For a parallel‑plate capacitor, C = ε₀ εᵣ A / d, where A is plate area, d is separation, and εᵣ is the relative permittivity of the dielectric.
平行板电容器的电容为 C = ε₀ εᵣ A / d，A 为极板面积，d 为间距，εᵣ 为介质的相对介电常数。
When capacitors are combined in series, 1/C_total = 1/C₁ + 1/C₂ + …; in parallel, C_total = C₁ + C₂ + … . The time constant for an RC circuit is τ = R C, governing the rate of charging and discharging.
电容器串联时，1/C_total = 1/C₁ + 1/C₂ + …；并联时，C_total = C₁ + C₂ + … 。RC 电路的时间常数 τ = R C，决定了充放电的速率。
7. Magnetic Fields | 磁场
A current‑carrying conductor experiences a force in a magnetic field given by F = B I L sinθ (Fleming’s left‑hand rule). For a moving charge, the force is F = B q v sinθ.
载流导体在磁场中受力为 F = B I L sinθ（弗莱明左手定则）。运动电荷受力为 F = B q v sinθ。
The magnetic flux density B is measured in tesla. The magnetic flux Φ through a surface is Φ = B A cosθ, and flux linkage is N Φ.
磁通量密度 B 的单位为特斯拉。穿过某面的磁通量 Φ = B A cosθ，磁链为 N Φ。
A charged particle moving perpendicular to a uniform magnetic field undergoes circular motion with radius r = m v / (B q) and period T = 2π m / (B q). The Hall effect gives a voltage V_H = B I / (n q t) across a conductor.
带电粒子垂直射入匀强磁场做圆周运动，半径 r = m v / (B q)，周期 T = 2π m / (B q)。霍尔效应在导体两端产生电压 V_H = B I / (n q t)。
8. Electromagnetic Induction | 电磁感应
Faraday’s law states that the induced e.m.f. is equal to the rate of change of magnetic flux linkage: ε = – N ΔΦ / Δt. Lenz’s law determines the direction: the induced current opposes the change that produced it.
法拉第定律指出，感应电动势等于磁链的变化率：ε = – N ΔΦ / Δt。楞次定律确定方向：感应电流阻碍引起它的变化。
For a conductor of length l moving at speed v perpendicular to a uniform field B, the induced e.m.f. is ε = B l v. In an AC generator, the e.m.f. varies sinusoidally: ε = ε₀ sin(ωt).
长度为 l 的导线以速度 v 垂直于匀强磁场 B 运动时，感应电动势 ε = B l v。交流发电机中，电动势按正弦变化：ε = ε₀ sin(ωt)。
Transformers change AC voltages according to V_s / V_p = N_s / N_p, assuming ideal flux linkage. Eddy currents in solid cores are minimised by lamination.
理想磁链下，变压器按 V_s / V_p = N_s / N_p 变换电压。通过铁芯叠片可减小涡流。
9. Alternating Currents | 交流电
An alternating current (AC) varies with time, usually described as I = I₀ sin(ωt). The root‑mean‑square (r.m.s.) value for a sinusoidal current is I_rms = I₀ / √2, and similarly V_rms = V₀ / √2.
交流电随时间变化，通常表示为 I = I₀ sin(ωt)。正弦电流的方均根值为 I_rms = I₀ / √2，同理 V_rms = V₀ / √2。
The average power in an AC circuit is P = I_rms V_rms cos φ, where cos φ is the power factor. In purely resistive loads, the phase angle φ = 0°, so all power is dissipated.
交流电路的平均功率为 P = I_rms V_rms cos φ，cos φ 为功率因数。纯电阻负载中，相位角 φ = 0°，功率完全耗散。
A diode allows half‑wave or full‑wave rectification, smoothing using a capacitor produces a nearly steady DC voltage. The ripple voltage is reduced by larger capacitance or load resistance.
二极管可实现半波或全波整流，用电容器滤波后产生接近稳定的直流电压。增大电容或负载电阻可减小纹波电压。
10. Quantum Physics | 量子物理
The photoelectric effect demonstrates that light consists of photons with energy E = h f, where h is Planck’s constant. The maximum kinetic energy of emitted electrons is K_max = h f – Φ, where Φ is the work function.
光电效应表明光由光子组成，光子能量 E = h f，h 为普朗克常量。发射电子的最大动能为 K_max = h f – Φ，Φ 为功函数。
Electron diffraction confirms the wave nature of particles; the de Broglie wavelength is λ = h / p, where p is momentum. This is observed when electrons pass through a crystal lattice or thin film.
电子衍射证实粒子的波动性；德布罗意波长为 λ = h / p，p 为动量。电子穿过晶格或薄膜时可观察到这一现象。
Spectral lines in atomic emission or absorption spectra arise from transitions between discrete energy levels: ΔE = h f. The energy levels in a hydrogen atom are given by E_n = –13.6 / n² eV.
原子发射或吸收光谱中的谱线源于离散能级间的跃迁：ΔE = h f。氢原子能级公式为 E_n = –13.6 / n² eV。
11. Nuclear Physics | 核物理
The nucleus is described by its proton number Z and nucleon number A. Nuclear radii follow roughly R = r₀ A^(1/3), where r₀ ≈ 1.2 fm. Nuclear density is approximately constant.
原子核由质子数 Z 与核子数 A 描述。核半径近似为 R = r₀ A^(1/3)，r₀ ≈ 1.2 fm。核密度近似恒定。
Radioactive decay follows the exponential law N = N₀ e^(–λt), with half‑life T½ = ln 2 / λ. The activity A = λ N. Alpha, beta, and gamma emissions have distinct properties and ionising abilities.
放射性衰变遵循指数规律 N = N₀ e^(–λt)，半衰期 T½ = ln 2 / λ。放射性活度 A = λ N。α、β 与 γ 射线具有不同的性质和电离能力。
Nuclear reactions conserve charge and nucleon number. For example, a typical fission reaction:
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n
The energy released is calculated from mass defect using E = Δm c².
核反应遵循电荷数与核子数守恒。例如，一个典型的裂变反应如上所示。释放的能量由质量亏损按 E = Δm c² 计算。
12. Medical Physics | 医学物理
Ultrasound imaging uses high‑frequency sound waves (f > 20 kHz). The acoustic impedance Z = ρ c determines reflection at tissue boundaries. The intensity reflection coefficient for normal incidence is α = (Z₂ – Z₁)² / (Z₂ + Z₁)².
超声成像使用高频声波（f > 20 kHz）。声阻抗 Z = ρ c 决定了组织界面的反射。垂直入射时的强度反射系数为 α = (Z₂ – Z₁)² / (Z₂ + Z₁)²。
X‑rays are produced when high‑energy electrons hit a metal target. The attenuation of X‑rays follows I = I₀ e^(–μ x), where μ is the linear attenuation coefficient. CT scanners create cross‑sectional images by combining multiple projections.
X 射线由高能电子轰击金属靶产生。X 射线的衰减遵循 I = I₀ e^(–μ x)，μ 为线性衰减系数。CT 扫描仪通过多角度投影组合生成断层图像。
In nuclear medicine, gamma‑emitting radioisotopes such as technetium‑99m are used as tracers. The gamma camera detects photons to construct an image of organ function. The half‑life of the isotope must be short to minimise patient dose.
核医学使用
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