📚 Core Knowledge Summary for Year 13 Edexcel Physics | Year 13 Edexcel 物理核心知识点梳理
Year 13 Edexcel Physics builds on AS foundations to deepen your understanding of mechanics, fields, thermodynamics, and modern physics. This article distils the essential topics and equations you must master for the A-level exams, presenting each concept in a clear, bilingual format.
Year 13 Edexcel 物理在 AS 基础上深化了对力学、场、热力学和现代物理的理解。本文浓缩了 A-level 考试必须掌握的核心主题和方程式，以清晰的中英双语形式呈现每个概念。
1. Further Mechanics: Momentum and Circular Motion | 进阶力学：动量与圆周运动
In further mechanics, the principle of conservation of linear momentum states that in a closed system with no external forces, total momentum before a collision equals total momentum after: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. Impulse equals the change in momentum, FΔt = Δp, which links force to momentum transfer.
在进阶力学中，动量守恒定律指出，在无外力的封闭系统内，碰撞前的总动量等于碰撞后的总动量：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。冲量等于动量的变化量，FΔt = Δp，将力与动量传递联系起来。
An object moving in a circle with constant speed experiences a centripetal acceleration a = v²/r towards the centre. The centripetal force F = mv²/r = mω²r, where ω is the angular velocity in rad s⁻¹, ω = 2π/T.
物体以恒定速率作圆周运动时，会受到指向圆心的向心加速度 a = v²/r。向心力为 F = mv²/r = mω²r，其中角速度 ω 的单位为 rad s⁻¹，ω = 2π/T。
2. Electric Fields and Coulomb’s Law | 电场与库仑定律
Electric field strength E is defined as the force per unit positive charge, E = F/Q. For a point charge, the radial field strength is given by E = kQ/r², where k = 1/(4πε₀). Uniform electric fields between parallel plates produce a constant field E = V/d, where V is the potential difference and d is the plate separation.
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，径向电场强度由 E = kQ/r² 给出，其中 k = 1/(4πε₀)。平行板之间的匀强电场产生恒定的场强 E = V/d，V 是电势差，d 是板间距。
The electric potential V at a point in a radial field is the work done per unit charge to bring a positive test charge from infinity to that point: V = kQ/r. The potential energy of two charges is U = kQ₁Q₂/r. Equipotential surfaces are perpendicular to field lines, and no work is done when moving along them.
径向场中某点的电势 V 是将单位正电荷从无穷远移至该点所做的功：V = kQ/r。两电荷的电势能为 U = kQ₁Q₂/r。等势面垂直于电场线，沿等势面移动电荷时不做功。
3. Capacitance and Energy Storage | 电容与能量存储
Capacitance C is the charge stored per unit potential difference, C = Q/V. For a parallel‑plate capacitor, C = ε₀A/d, where A is the plate area and d is the separation. When a dielectric of relative permittivity εᵣ is inserted, capacitance increases to C = εᵣε₀A/d.
电容 C 是单位电势差下储存的电荷量，C = Q/V。对于平行板电容器，C = ε₀A/d，其中 A 是板面积，d 是间距。插入相对介电常数为 εᵣ 的介质后，电容增大为 C = εᵣε₀A/d。
The energy stored in a capacitor can be expressed as E = ½QV = ½CV² = ½Q²/C. When capacitors are combined in parallel, C_total = C₁ + C₂; in series, 1/C_total = 1/C₁ + 1/C₂. The time constant τ = RC governs the rate of charging and discharging: V = V₀e⁻ᵗ/ᴿᶜ during discharge.
电容器储存的能量可表示为 E = ½QV = ½CV² = ½Q²/C。电容器并联时，总电容 C_total = C₁ + C₂；串联时，1/C_total = 1/C₁ + 1/C₂。时间常数 τ = RC 决定充放电速率：放电时 V = V₀e⁻ᵗ/ᴿᶜ。
4. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
A magnetic field exerts a force on a moving charge: F = BQv sin θ, where B is the magnetic flux density, v is the velocity, and θ is the angle between v and B. For a current‑carrying conductor of length L, F = BIL sin θ. Fleming’s left‑hand rule gives the direction of force.
磁场对运动电荷施加力的作用：F = BQv sin θ，其中 B 是磁通量密度，v 是速度，θ 是 v 与 B 之间的夹角。对于长度为 L 的载流导体，F = BIL sin θ。左手定则给出力的方向。
Faraday’s law states that the induced emf in a circuit is equal to the rate of change of magnetic flux linkage: ε = –N dΦ/dt. Lenz’s law (the minus sign) indicates that the induced current opposes the change in flux. Magnetic flux Φ = BA cos θ, and flux linkage is NΦ. A coil rotating in a magnetic field generates an alternating emf.
法拉第定律指出，电路中感应电动势的大小等于磁通链变化率的负值：ε = –N dΦ/dt。楞次定律（负号）表明感应电流阻碍磁通量的变化。磁通量 Φ = BA cos θ，磁通链为 NΦ。磁场中转动的线圈会产生交变电动势。
5. Nuclear Physics and the Standard Model | 核物理与标准模型
The nucleus is composed of protons and neutrons (nucleons), held together by the strong nuclear force. The radius of a nucleus depends on its mass number A: R = r₀A^(1/3), where r₀ ≈ 1.2 fm. Nuclear density is approximately constant and extremely high, around 2×10¹⁷ kg m⁻³.
原子核由质子和中子（核子）组成，靠强核力结合在一起。核半径依赖于质量数 A：R = r₀A^(1/3)，r₀ ≈ 1.2 fm。核密度近似为常数且极高，约为 2×10¹⁷ kg m⁻³。
Einstein’s mass–energy equivalence, ΔE = Δm c², explains the binding energy of a nucleus – the energy required to separate it into its constituents. The binding energy per nucleon peaks around iron‑56, making it the most stable nucleus. Fusion combines light nuclei; fission splits heavy nuclei, both releasing energy.
爱因斯坦的质能方程 ΔE = Δm c² 解释了原子核的结合能——将核子分开所需的能量。每个核子的平均结合能在铁‑56 附近达到峰值，使其成为最稳定的原子核。聚变将轻核合并，裂变将重核分裂，两者都释放能量。
6. Thermodynamics and Ideal Gases | 热力学与理想气体
The internal energy of a system is the sum of the random kinetic and potential energies of its particles. The first law of thermodynamics states ΔU = Q – W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
系统的内能是其粒子无规则运动的动能与势能之和。热力学第一定律表述为 ΔU = Q – W，其中 ΔU 是内能变化量，Q 是系统吸收的热量，W 是系统对外做的功。
An ideal gas obeys the equation pV = nRT, where n is the number of moles and R = 8.31 J mol⁻¹ K⁻¹. The kinetic theory links macroscopic pressure to microscopic motion: pV = ⅓ N m
理想气体遵循状态方程 pV = nRT，n 为摩尔数，R = 8.31 J mol⁻¹ K⁻¹。分子动理论将宏观压强与微观运动联系起来：pV = ⅓ N m
7. Gravitational Fields | 引力场
Newton’s law of gravitation gives the force between two point masses: F = Gm₁m₂/r². Gravitational field strength g is the force per unit mass, and for a radial field around a mass M, g = GM/r². Near the Earth’s surface, g ≈ 9.81 N kg⁻¹ and the field is approximately uniform.
牛顿万有引力定律给出两个质点之间的引力：F = Gm₁m₂/r²。引力场强度 g 是单位质量所受的力，对于质量 M 的径向场，g = GM/r²。接近地球表面时，g ≈ 9.81 N kg⁻¹，引力场近似为匀强场。
Gravitational potential V_g = –GM/r, defined as the work done per unit mass to bring a mass from infinity to that point. The potential energy of a mass m in the field is U = –GMm/r. Escape velocity from the surface of a planet is v_esc = √(2GM/R), derived from energy conservation.
引力势 V_g = –GM/r，定义为将单位质量从无穷远移至该点所做的功。质量为 m 的物体在引力场中的势能为 U = –GMm/r。行星表面的逃逸速度 v_esc = √(2GM/R)，由能量守恒推导得出。
8. Simple Harmonic Motion | 简谐运动
Simple harmonic motion (SHM) occurs when the restoring force is proportional to the displacement and directed towards equilibrium: F = –kx. The acceleration obeys a = –ω²x, where ω is the angular frequency. The displacement can be expressed as x = A cos(ωt) or x = A sin(ωt), with A the amplitude.
简谐运动（SHM）发生在回复力与位移成正比且指向平衡位置时：F = –kx。加速度遵循 a = –ω²x，ω 为角频率。位移可表示为 x = A cos(ωt) 或 x = A sin(ωt)，A 为振幅。
Key relationships include the period of a mass–spring system T = 2π√(m/k) and a simple pendulum T = 2π√(L/g). The velocity in SHM is v = ±ω√(A² – x²), and maximum values are v_max = ωA, a_max = ω²A. Energy continuously exchanges between kinetic and potential forms, but the total energy remains constant: E_total = ½ m ω² A².
关键关系式包括弹簧振子的周期 T = 2π√(m/k) 和单摆的周期 T = 2π√(L/g)。SHM 中的速度为 v = ±ω√(A² – x²)，最大值为 v_max = ωA，a_max = ω²A。能量在动能和势能之间持续转换，但总能量保持不变：E_total = ½ m ω² A²。
9. Astrophysics and Cosmology | 天体物理与宇宙学
The luminosity of a star L is the total power radiated, related to its surface temperature T by the Stefan–Boltzmann law: L = 4πR² σ T⁴, where σ = 5.67×10⁻⁸ W m⁻² K⁻⁴ and R is the stellar radius. Wien’s displacement law gives the peak wavelength of radiation: λ_max T = 2.898×10⁻³ m K.
恒星的光度 L 是其总辐射功率，通过斯特藩-玻尔兹曼定律与表面温度 T 关联：L = 4πR² σ T⁴，其中 σ = 5.67×10⁻⁸ W m⁻² K⁻⁴，R 为恒星半径。维恩位移定律给出辐射峰值波长：λ_max T = 2.898×10⁻³ m K。
Hubble’s law describes the expansion of the Universe: v = H₀ d, where v is the recessional velocity, d is the distance, and H₀ is the Hubble constant. The Big Bang theory is supported by cosmic microwave background radiation and the predominance of light elements. Dark matter and dark energy are proposed to explain galactic rotation curves and accelerating expansion.
哈勃定律描述了宇宙的膨胀：v = H₀ d，其中 v 为退行速度，d 为距离，H₀ 为哈勃常数。宇宙微波背景辐射和轻元素丰度为宇宙大爆炸理论提供了证据。暗物质和暗能量被提出以解释星系旋转曲线和加速膨胀。
10. Nuclear Radiation and Decay | 核辐射与衰变
Unstable nuclei decay via alpha, beta, or gamma emission. Alpha particles are helium nuclei, beta particles are fast electrons (β⁻) or positrons (β⁺), and gamma rays are high‑energy photons. The activity A = λN, where λ is the decay constant, and radioactive decay follows the exponential law N = N₀ e⁻λᵗ.
不稳定原子核通过 α、β 或 γ 发射衰变。α 粒子是氦核，β 粒子是快电子（β⁻）或正电子（β⁺），γ 射线是高能光子。活度 A = λN，λ 是衰变常数，放射性衰变遵循指数规律 N = N₀ e⁻λᵗ。
The half‑life T_½ = ln2/λ is the time for half of the nuclei to decay. In β⁻ decay, a neutron turns into a proton with emission of an electron and an antineutrino; in β⁺ decay, a proton turns into a neutron with a positron and a neutrino. The neutrino hypothesis conserves energy and momentum in beta decay.
半衰期 T_½ = ln2/λ 是一半原子核衰变所需的时间。在 β⁻ 衰变中，一个中子转变为质子，同时放出一个电子和一个反中微子；在 β⁺ 衰变中，一个质子转变为中子，放出一个正电子和一个中微子。中微子假说确保了 β 衰变中能量和动量守恒。
Published by TutorHao | Physics Revision Series | aleveler.com
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