📚 Year 13 Edexcel Physics: Quick Reference Handbook of Formulas & Theorems | Year 13 Edexcel 物理公式定理速查手册
This handbook provides a concise, topic-by-topic compilation of the essential formulas, laws and definitions you need for the Year 13 Edexcel Physics examinations. Every equation is presented in a way that reflects the style of your data booklet and exam questions, with brief reminders of the underlying concepts. Work through each section to build fluency and recall – and always remember to check units, sign conventions and vector directions when applying these results.
这本速查手册按主题为你梳理了 Year 13 Edexcel 物理考试中最关键的公式、定律与定义。每一组公式都采用了与考试数据手册和真题相似的风格呈现，并附有概念要点的简短提醒。逐节复习可以帮助你提升熟练度和记忆准确度——在应用这些结果时，请务必留意单位、正负号约定以及矢量的方向。
1. Further Mechanics | 进阶力学
Linear momentum is conserved in all collisions and explosions, provided no external resultant force acts. The impulse delivered by a force equals the change in momentum.
只要系统不受外力作用，线动量在任何碰撞和爆炸过程中都守恒。力的冲量等于动量的变化量。
p = mv
Impulse = FΔt = Δp = mv – mu
Kinetic energy may or may not be conserved – compare elastic collisions (KE conserved) with inelastic collisions (KE not conserved).
动能不一定守恒——弹性碰撞中动能守恒，非弹性碰撞中动能不守恒。
For an object moving in a circle at constant speed, the velocity direction changes continuously, giving rise to a centripetal acceleration directed towards the centre.
做匀速圆周运动的物体，其速度方向时刻改变，因此存在指向圆心的向心加速度。
a = v²/r = rω²
F = mv²/r = mrω²
Here ω is the angular speed (ω = 2πf = Δθ/Δt). The centripetal force is not a separate type of force; it is provided by tension, gravity, friction or the normal reaction.
式中 ω 为角速度（ω = 2πf = Δθ/Δt）。向心力不是一种独立的力，它可以由拉力、重力、摩擦力或支持力提供。
2. Electric Fields | 电场
Coulomb’s law gives the force between two point charges. Like charges repel; unlike charges attract. The permittivity of free space is ε₀ = 8.85 × 10⁻¹² F m⁻¹.
库仑定律描述两个点电荷之间的作用力。同号电荷相斥，异号电荷相吸。真空介电常量 ε₀ = 8.85 × 10⁻¹² F m⁻¹。
F = kQ₁Q₂/r² = (1/4πε₀)Q₁Q₂/r²
Electric field strength E at a point is the force per unit positive charge. For a radial field around a point charge Q, and for a uniform field between parallel plates separated by distance d:
电场强度 E 定义为单位正电荷所受的力。点电荷 Q 的径向电场，以及相距 d 的平行板间的匀强电场分别满足：
E = F/q
E = Q/(4πε₀r²) (radial)
E = V/d (uniform)
Electric potential V is the work done per unit charge in bringing a positive test charge from infinity to that point. Potential is a scalar; field strength is the negative potential gradient.
电势 V 定义为单位正电荷从无穷远处移到该点过程中外力所做的功。电势是标量；电场强度是电势梯度的负值。
V = Q/(4πε₀r) (around a point charge)
E = –dV/dr
The work done in moving a charge q through a potential difference ΔV is W = qΔV.
电荷 q 在电势差 ΔV 中运动时，电场力做功为 W = qΔV。
3. Capacitors | 电容器
Capacitance C is the charge stored per unit potential difference. The energy stored in a capacitor is the area under a Q–V graph.
电容 C 定义为单位电势差下储存的电荷量。电容器储存的能量等于 Q–V 图线下的面积。
C = Q/V
W = ½QV = ½CV² = ½Q²/C
For a parallel-plate capacitor, capacitance is proportional to the plate area A and inversely proportional to the separation d.
平行板电容器的电容与极板面积 A 成正比，与极板间距 d 成反比。
C = ε₀εᵣA/d
The charging and discharging of a capacitor through a resistor follow exponential laws with time constant τ = RC.
通过电阻充放电时，电容器的电压、电荷与电流随时间按指数规律变化，时间常数 τ = RC。
Q = Q₀e^(–t/RC), V = V₀e^(–t/RC) (discharge)
I = I₀e^(–t/RC)
When t = τ, the quantity falls to about 37% of its initial value; after 5τ the capacitor is considered fully charged or discharged.
当 t = τ 时，数值降至初始值的约 37%；经过 5τ 后可以认为充放电过程基本完成。
4. Magnetic Fields | 磁场
A magnetic field exerts a force on a moving charge. Fleming’s left‑hand rule gives the direction of the force for a conventional current.
磁场对运动电荷有力的作用。左手定则（弗莱明左手定则）可以确定正电荷或电流所受安培力的方向。
F = Bqv sinθ (single charge)
F = BIL sinθ (current-carrying wire)
When a charged particle moves perpendicular to a uniform B field, it follows a circular path with radius r = mv/(Bq).
当带电粒子垂直于匀强磁场运动时，它将做匀速圆周运动，半径 r = mv/(Bq)。
Magnetic flux Φ and flux density B are linked by Φ = BA cosθ. Faraday’s law states that the magnitude of the induced e.m.f. equals the rate of change of magnetic flux linkage. Lenz’s law determines the direction of the induced current.
磁通量 Φ 与磁通密度 B 的关系为 Φ = BA cosθ。法拉第电磁感应定律指出，感应电动势的大小等于磁链的变化率。楞次定律决定了感应电流的方向。
ε = –N ΔΦ/Δt
Induced e.m.f. can be motional (ε = BLv for a conductor moving perpendicular to the field) or due to changing B or area.
感应电动势可以是动生的（导线垂直切割磁感线时 ε = BLv），也可以由变化的磁场或回路面积引起。
For an ideal transformer, the ratios of voltages and currents relate to the turns ratio.
理想变压器中，电压比和电流比与匝数比的关系为：
Vₛ/Vₚ = Nₛ/Nₚ = Iₚ/Iₛ
5. Nuclear Physics | 核物理
Radioactive decay is a random, exponential process characterised by the decay constant λ. The number of undecayed nuclei N follows:
放射性衰变是随机的指数过程，由衰变常量 λ 表征。未衰变原子核数目 N 满足：
N = N₀e^(–λt)
A = λN, A = A₀e^(–λt)
Half‑life T½ is related to λ by T½ = ln 2/λ ≈ 0.693/λ.
半衰期 T½ 与 λ 的关系为 T½ = ln 2/λ ≈ 0.693/λ。
The mass defect Δm is the difference between the mass of the separated nucleons and the mass of the nucleus. Binding energy Eb = Δm c².
质量亏损 Δm 是核子单独存在时的总质量与原子核质量之差。结合能 Eb = Δm c²。
The binding energy per nucleon curve peaks around iron‑56; fusion of light nuclei and fission of heavy nuclei are both energetically favourable.
比结合能曲线在铁‑56 附近达到峰值；轻核聚变和重核裂变在能量上都是有利的。
In nuclear reactions, mass–energy, charge and nucleon number are conserved.
在核反应中，质能守恒、电荷数守恒和核子数守恒成立。
6. Thermal Physics | 热物理
The ideal gas equation links pressure p, volume V, number of moles n and absolute temperature T. The Boltzmann constant k = 1.38 × 10⁻²³ J K⁻¹; R = 8.31 J mol⁻¹ K⁻¹.
理想气体状态方程联系了压强 p、体积 V、物质的量 n 和绝对温度 T。玻尔兹曼常量 k = 1.38 × 10⁻²³ J K⁻¹；气体常量 R = 8.31 J mol⁻¹ K⁻¹。
pV = nRT = NkT
The kinetic theory model relates the average translational kinetic energy of a molecule to the absolute temperature.
分子动理论模型将分子的平均平动动能与绝对温度联系起来。
½ m〈c²〉 = (3/2)kT
pV = ⅓ N m〈c²〉
The internal energy U of an ideal gas is the sum of the random kinetic energies of its molecules; it depends only on temperature.
理想气体的内能 U 是其分子无规则运动动能的总和，只与温度有关。
The first law of thermodynamics is a statement of energy conservation for a system.
热力学第一定律是能量守恒定律在热学系统中的表达。
ΔU = Q + W
Here W is the work done on the system (W = –pΔV for expansion at constant pressure). Sign conventions must be applied consistently.
式中 W 为外界对系统做的功（恒压膨胀时 W = –pΔV）。使用中需遵循统一的正负号约定。
7. Gravitational Fields | 引力场
Newton’s law of gravitation describes the attractive force between two point masses. The gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
牛顿万有引力定律描述两质点间的吸引力。引力常量 G = 6.67 × 10⁻¹¹ N m² kg⁻²。
F = –GMm/r²
Gravitational field strength g at a point is the force per unit mass. For a spherical mass M, the field outside is radial and identical to that of a point mass at the centre.
引力场强度 g 定义为单位质量所受的万有引力。在球形天体外部，引力场与质量全部集中到球心所产生的场相同。
g = F/m = GM/r² (radial field)
Gravitational potential Vg is the work done per unit mass in bringing a test mass from infinity to that point; it is always negative near a mass.
引力势 Vg 是单位质量从无穷远移到该点外力所做的功；在质量附近引力势总为负值。
Vg = –GM/r
g = –dVg/dr
For circular orbits, the centripetal force is provided by gravity, yielding Kepler’s third law.
圆形轨道上，万有引力提供向心力，由此可导出开普勒第三定律。
T² ∝ r³, T² = (4π²/GM) r³
8. Oscillations | 振动
Simple harmonic motion occurs when the restoring force (or acceleration) is proportional to the displacement from equilibrium and directed towards it.
当回复力（或加速度）与离开平衡位置的位移成正比且方向指向平衡位置时，物体做简谐运动。
a = –ω²x
The displacement, velocity and acceleration as functions of time can be written using sine or cosine functions.
位移、速度和加速度随时间的变化可用正弦或余弦函数描述。
x = A cos(ωt) or x = A sin(ωt)
v = ±ω√(A² – x²)
v_max = ωA, a_max = ω²A
The period T is independent of amplitude for small oscillations. For a mass–spring system and a simple pendulum:
对于小振幅振动，周期 T 与振幅无关。常见系统的周期公式如下：
T = 2π√(m/k) (mass–spring)
T = 2π√(l/g) (simple pendulum)
The total energy of an undamped simple harmonic oscillator is constant and proportional to the square of the amplitude.
无阻尼简谐振子的总能量保持恒定，且与振幅的平方成正比。
E_total = ½ mω²A²
Damping removes energy; light damping gives a gradual decrease in amplitude, while critical and heavy damping alter the motion in distinctive ways. Resonance occurs when the driving frequency equals the natural frequency, producing a maximum amplitude.
阻尼会耗散能量；弱阻尼使振幅逐渐减小，临界阻尼和过阻尼则以不同方式改变运动状态。当驱动频率等于系统固有频率时发生共振，振幅达到最大。
9. Astrophysics and Cosmology | 天体物理与宇宙学
The luminosity L of a star is the total power radiated. The observed intensity (flux) F at Earth depends on the inverse‑square law.
恒星光度 L 是其向外辐射的总功率。地球上观测到的辐射通量 F 遵循平方反比定律。
F = L/(4πd²)
Standard candles, such as Cepheid variables, allow distance determination because their luminosity is known from their period.
标准烛光（如造父变星）由于光变周期与光度相关，可以用来测定天体的距离。
Wien’s displacement law and the Stefan–Boltzmann law link the temperature of a black‑body star to its peak wavelength and luminosity.
维恩位移定律和斯特藩‑玻尔兹曼定律将黑体恒星的有效温度与峰值波长及光度联系起来。
λ_max T = 2.898 × 10⁻³ m K
L = 4πR² σT⁴ (σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴)
Hubble’s law describes the expansion of the Universe: recessional velocity is proportional to distance. The Hubble constant H₀ is currently estimated at about 70 km s⁻¹ Mpc⁻¹.
哈勃定律描述了宇宙膨胀：退行速度与距离成正比。哈勃常数 H₀ 目前的估值约为 70 km s⁻¹ Mpc⁻¹。
v = H₀d
Cosmological redshift z is given by z = Δλ/λ₀ ≈ v/c for v ≪ c. The age and ultimate fate of the Universe depend on the precise value of H₀ and the density of mass‑energy.
宇宙学红移 z = Δλ/λ₀，在 v ≪ c 时近似为 v/c。宇宙的年龄和最终命运取决于 H₀ 的精确值以及质能密度。
10. Particle Physics | 粒子物理
Hadrons feel the strong nuclear force; they are subdivided into baryons (3 quarks, e.g. proton uud, neutron udd) and mesons (quark–antiquark pairs).
强子参与强相互作用，分为重子（3个夸克，如质子 uud，中子 udd）和介子（夸克‑反夸克对）。
Leptons (electron, muon, neutrinos) do not feel the strong force. Conservation laws – charge, baryon number, lepton number, and strangeness (in strong interactions) – must be satisfied.
轻子（电子、μ子、中微子）不参与强相互作用。守恒定律——电荷、重子数、轻子数和奇异数（在强相互作用中）必须被满足。
The exchange particles for the four fundamental forces are: photon (electromagnetic), W⁺/W⁻/Z⁰ (weak), gluon (strong), and the hypothetical graviton (gravity).
四种基本相互作用的媒介粒子分别是：光子（电磁力）、W⁺/W⁻/Z⁰ 玻色子（弱力）、胶子（强力）和假想的引力子（引力）。
In β⁻ decay, a neutron becomes a proton with the emission of an electron and an anti‑electron‑neutrino: n → p + e⁻ + ν̄ₑ.
在 β⁻ 衰变中，中子转化为质子，同时放出一个电子和一个反电子中微子：n → p + e⁻ + ν̄ₑ。
Quarks have fractional charges (+⅔e or –⅓e) and are confined within hadrons. Particle interactions are visualised using Feynman diagrams.
夸克带有分数电荷（+⅔e 或 –⅓e）并被禁闭在强子内部。粒子间的相互作用可以用费曼图直观表示。
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