Year 13 Edexcel Physics: Formula & Theorem Quick Reference Handbook | Edexcel 13年级物理：公式定理速查手册

📚 Year 13 Edexcel Physics: Formula & Theorem Quick Reference Handbook | Edexcel 13年级物理：公式定理速查手册

This handbook provides a concise, topic-by-topic summary of the essential formulas and theorems for Year 13 Edexcel Physics. Use it for last-minute revision, exam practice, and to ensure every key relationship is at your fingertips. All formulas are expressed in clear Unicode symbols for readability and quick reference.

本手册按主题简明汇总了 Edexcel 13 年级物理的核心公式与定理，适用于考前冲刺、习题演练，确保你对每一个重要关系都了如指掌。所有公式均采用清晰的 Unicode 符号表示，便于阅读和快速查阅。

1. Further Mechanics: Circular Motion | 进阶力学：圆周运动

Angular displacement, angular speed, and the centripetal acceleration are cornerstones of circular motion. Remember that even when speed is constant, velocity changes due to direction, giving rise to a net inward force.

角位移、角速度和向心加速度是圆周运动的基石。注意，即使速率不变，因方向持续变化，速度矢量也在变化，从而产生指向圆心的合力。

• Angular speed ω = 2π / T = 2πf

  角速度 ω = 2π/T = 2πf

• Linear speed v = r ω

  线速度 v = r ω

• Centripetal acceleration a = v² / r = r ω²

  向心加速度 a = v² / r = r ω²

• Centripetal force F = m v² / r = m r ω²

  向心力 F = m v² / r = m r ω²

• Frequency f = 1 / T

  频率 f = 1/T

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2. Simple Harmonic Motion (SHM) | 简谐运动

SHM is defined by acceleration being proportional to negative displacement. The key equations describe displacement, velocity, acceleration, and energy interchange. The mass‑spring system and simple pendulum both exhibit SHM under small amplitudes.

简谐运动的特征是加速度与位移成正比且方向相反。关键方程描述了位移、速度、加速度以及能量转换。弹簧振子和单摆在小振幅下都做简谐运动。

• a = – ω² x (defining equation)

  a = – ω² x （定义方程）

• Displacement x = A cos(ω t) or x = A sin(ω t)

  位移 x = A cos(ω t) 或 x = A sin(ω t)

• Velocity v = ± ω √(A² – x²)

  速度 v = ± ω √(A² – x²)

• Maximum speed v_max = ω A

  最大速率 v_max = ω A

• Period for mass‑spring system T = 2π √(m / k)

  弹簧振子周期 T = 2π √(m / k)

• Period for simple pendulum T = 2π √(L / g)

  单摆周期 T = 2π √(L / g)

• Total energy E_total = ½ m ω² A²

  总能量 E_total = ½ m ω² A²

• Kinetic energy E_k = ½ m ω² (A² – x²)

  动能 E_k = ½ m ω² (A² – x²)

• Potential energy E_p = ½ m ω² x²

  势能 E_p = ½ m ω² x²

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3. Gravitational Fields | 引力场

Newton’s law of gravitation and the concept of gravitational potential are central to understanding orbits, satellite motion, and escape velocity. Gravitational field strength g is the force per unit mass at a point.

牛顿万有引力定律和引力势的概念是理解轨道运动、卫星运行和逃逸速度的关键。引力场强度 g 是单位质量在该点所受的力。

• Newton’s law: F = G M m / r²

  万有引力定律：F = G M m / r²

• Field strength g = GM / r²

  场强 g = GM / r²

• Gravitational potential V_g = – GM / r (set zero at infinity)

  引力势 V_g = – GM / r （无穷远处为零）

• Potential energy U = m V_g = – G M m / r

  引力势能 U = m V_g = – G M m / r

• Kepler’s Third Law T² ∝ r³, or for circular orbits: T² = (4π² / GM) r³

  开普勒第三定律 T² ∝ r³，圆轨道时：T² = (4π² / GM) r³

• Escape velocity v_esc = √(2GM / R)

  逃逸速度 v_esc = √(2GM / R)

• Orbital speed for circular orbit v = √(GM / r)

  圆轨道速度 v = √(GM / r)

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4. Electric Fields | 电场

Electric fields arise from static charges; Coulomb’s law describes the force between point charges. Field strength E is the force per unit positive charge. Key analogues exist with gravitational fields, but note the sign difference for potential.

电场由静止电荷产生；库仑定律描述了点电荷之间的作用力。电场强度 E 是单位正电荷所受的力。与引力场存在重要类比，但需留意势的符号差异。

• Coulomb’s law: F = k Q₁ Q₂ / r², where k = 1/(4π ε₀)

  库仑定律：F = k Q₁ Q₂ / r²，其中 k = 1/(4π ε₀)

• Electric field strength E = F / q = k Q / r²

  电场强度 E = F / q = k Q / r²

• Uniform field between parallel plates: E = V / d

  平行板间匀强电场：E = V / d

• Force on charge in uniform field F = q E

  电荷在匀强电场中的受力 F = q E

• Electric potential V_e = k Q / r (zero at infinity, sign of Q matters)

  电势 V_e = k Q / r （无穷远处为零，注意 Q 的符号）

• Potential energy of two charges U = k Q₁ Q₂ / r

  两点电荷势能 U = k Q₁ Q₂ / r

• Work done W = q ΔV

  电场力做功 W = q ΔV

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5. Capacitance | 电容

Capacitors store energy in an electric field. The defining equation, the energy stored, and the exponential charging/discharging curves are essential. Time constant RC determines the rate of charge or discharge.

电容器将能量储存在电场中。定义式、储能公式以及指数充放电曲线是重点。时间常数 RC 决定了充放电的快慢。

• Capacitance C = Q / V

  电容定义式 C = Q / V

• Energy stored E = ½ Q V = ½ C V² = ½ Q² / C

  储能 E = ½ Q V = ½ C V² = ½ Q² / C

• Time constant τ = R C

  时间常数 τ = R C

• Charging: Q = Q₀ (1 – e^(–t / RC)), V = V₀ (1 – e^(–t / RC))

  充电：Q = Q₀ (1 – e^(–t / RC))，V = V₀ (1 – e^(–t / RC))

• Discharging: Q = Q₀ e^(–t / RC), V = V₀ e^(–t / RC)

  放电：Q = Q₀ e^(–t / RC)，V = V₀ e^(–t / RC)

• Current during discharge I = I₀ e^(–t / RC)

  放电电流 I = I₀ e^(–t / RC)

• Parallel plate capacitance C = ε₀ ε_r A / d

  平行板电容 C = ε₀ ε_r A / d

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6. Magnetic Fields | 磁场

Magnetic fields exert forces on moving charges and current‑carrying conductors. Fleming’s left‑hand rule gives force direction. A charged particle moving perpendicular to a uniform B field follows a circular path.

磁场对运动电荷和载流导线有力的作用。用左手定则判断力方向。带电粒子垂直于匀强磁场运动时做圆周运动。

• Force on a moving charge: F = B q v sin θ (Lorentz force)

  运动电荷受力：F = B q v sin θ （洛伦兹力）

• Force on a current‑carrying wire: F = B I L sin θ

  载流导线受力：F = B I L sin θ

• For θ = 90°, F = B q v and radius r = m v / (B q)

  当 θ = 90°，F = B q v，轨道半径 r = m v / (B q)

• Magnetic flux density B = F / (I L) (definition when perpendicular)

  磁感应强度 B = F / (I L) （垂直时定义）

• Magnetic flux Φ = B A cos θ

  磁通量 Φ = B A cos θ

• Flux linkage = N Φ

  磁链 = N Φ

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7. Electromagnetic Induction | 电磁感应

Faraday’s and Lenz’s laws govern induced emf. A changing magnetic flux through a coil induces an emf that opposes the change causing it. These principles underpin generators and transformers.

法拉第定律和楞次定律决定了感应电动势。穿过线圈的磁通量发生变化时，会产生反抗该变化的感应电动势。发电机和变压器均基于这一原理。

• Faraday’s law: ε = – N (dΦ / dt)

  法拉第定律：ε = – N (dΦ / dt)

• Magnitude of induced emf: |ε| = N |ΔΦ / Δt|

  感应电动势大小：|ε| = N |ΔΦ / Δt|

• Lenz’s law: the induced current flows to oppose the change in flux

  楞次定律：感应电流的方向总是反抗磁通量的变化

• Emf in a moving conductor: ε = B L v (perpendicular cut)

  运动导线切割磁感线：ε = B L v （垂直切割）

• Ideal transformer equation: V_s / V_p = n_s / n_p = I_p / I_s

  理想变压器公式：V_s / V_p = n_s / n_p = I_p / I_s

• Flux linkage and sinusoidal emf: ε = ε₀ sin ω t, where ε₀ = N B A ω

  磁链与正弦交变电动势：ε = ε₀ sin ω t，其中 ε₀ = N B A ω

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8. Nuclear Physics: Radioactivity and Binding Energy | 原子核物理：放射性与结合能

Nuclear stability, radioactive decay laws, and the mass‑energy equivalence are at the heart of this topic. The binding energy curve explains fission and fusion.

原子核的稳定性、放射性衰变规律以及质能关系是本部分的核心。结合能曲线解释了裂变和聚变。

• Mass‑energy equivalence: E = m c²

  质能方程：E = m c²

• Binding energy: E_b = Δm c², where Δm = (Z m_p + N m_n) – M_nucleus

  结合能：E_b = Δm c²，其中 Δm = (Z m_p + N m_n) – M_nucleus

• Radioactive decay law: N = N₀ e^(–λ t)

  衰变规律：N = N₀ e^(–λ t)

• Activity A = λ N = A₀ e^(–λ t)

  活度 A = λ N = A₀ e^(–λ t)

• Decay constant and half‑life: λ = ln 2 / t_½

  衰变常量与半衰期：λ = ln 2 / t_½

• Alpha decay: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

  α 衰变：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

• Beta‑minus decay: n → p + e⁻ + ν̅ₑ (example: ¹⁴₆C → ¹⁴₇N + e⁻ + ν̅ₑ)

  β⁻ 衰变：n → p + e⁻ + ν̅ₑ （如 ¹⁴₆C → ¹⁴₇N + e⁻ + ν̅ₑ）

• Nuclear fission chain reaction: ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n + energy

  核裂变链式反应：²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n + 能量

• Fusion example: ²H + ³H → ⁴He + n + energy

  聚变实例：²H + ³H → ⁴He + n + 能量

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9. Particle Physics: Fundamental Particles and Interactions | 粒子物理：基本粒子与相互作用

The Standard Model classifies particles into leptons, quarks, and gauge bosons. Conservation laws (charge, baryon number, lepton number) govern particle interactions.

标准模型将粒子分为轻子、夸克和规范玻色子。守恒定律（电荷、重子数、轻子数）支配着粒子间的相互作用。

• Quark combinations: proton (uud), neutron (udd), pion π⁺ (u d̅), kaon K⁺ (u s̅)

  夸克组合：质子 (uud)，中子 (udd)，π⁺ 介子 (u d̅)，K⁺ 介子 (u s̅)

• Beta decay in quarks: d → u + e⁻ + ν̅ₑ

  夸克层次的 β 衰变：d → u + e⁻ + ν̅ₑ

• Conservation of baryon number: each baryon = +1, antibaryon = –1

  重子数守恒：每个重子 +1，反重子 –1

• Conservation of lepton number: electron lepton number L_e conserved separately from muon and tau lepton numbers

  轻子数守恒：电子轻子数 L_e、μ 子轻子数、τ 子轻子数分别守恒

• Strangeness is conserved in strong interactions but not in weak interactions

  奇异数在强相互作用中守恒，在弱相互作用中不守恒

• Four fundamental forces: strong, electromagnetic, weak, gravitational (carried by gluons, photon, W⁺/W⁻/Z⁰, graviton)

  四种基本相互作用：强（胶子）、电磁（光子）、弱（W⁺/W⁻/Z⁰ 玻色子）、引力（引力子）

• Energy of photon: E = h f = h c / λ

  光子能量：E = h f = h c / λ

• Pair production: γ → e⁻ + e⁺ (requires E > 2 m_e c²)

  电子对产生：γ → e⁻ + e⁺ （需能量大于 2 m_e c²）

• Annihilation: e⁻ + e⁺ → 2γ (energy and momentum conservation)

  湮灭：e⁻ + e⁺ → 2γ（满足能量与动量守恒）

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10. Thermodynamics: Energy, Work and the First Law | 热力学：能量、功与第一定律

The first law of thermodynamics relates internal energy change to heat supplied and work done. Key processes include isothermal, adiabatic, isobaric, and isovolumetric. The ideal gas equation is a prerequisite.

热力学第一定律将内能的变化与供给的热量以及系统做功联系起来。重点过程包括等温、绝热、等压和等容过程。理想气体状态方程是基础。

• First law: ΔU = Q – W (where W = work done BY the system)

  第一定律：ΔU = Q – W（W 为系统对外做功）

• Work done during volume change at constant pressure: W = p ΔV

  恒压体积变化做功：W = p ΔV

• For a complete cycle, ΔU = 0, so Q_net = W_net

  完整循环中 ΔU = 0，故 Q_net = W_net

• Isothermal change: ΔU = 0, Q = W (pV = constant)

  等温过程：ΔU = 0，Q = W （pV = 常数）

• Adiabatic change: Q = 0, ΔU = –W (pV^γ = constant, TV^(γ–1) = constant)

  绝热过程：Q = 0，ΔU = –W （pV^γ = 常数，TV^(γ–1) = 常数）

• Ideal gas equation: p V = n R T = N k T

  理想气体状态方程：p V = n R T = N k T

• Kinetic theory pressure: p = ½ ρ or p V = ½ N m

  分子动理论压强：p = ½ ρ 或 p V = ⅓ N m

• Mean translational kinetic energy of a molecule: = (3/2) k T

  分子平均平动动能： = (3/2) k T

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11. Space: Astrophysics (Common Option) | 太空：天体物理（常见选修）

This optional topic explores luminosity, stellar distances, the Hertzsprung‑Russell diagram, and cosmological redshift. The key relationships link apparent magnitude, distance, and the expanding universe.

该选修单元探讨光度、恒星距离、赫罗图以及宇宙学红移。重要关系式将视星等、距离和宇宙膨胀联系起来。

• Inverse‑square law: I = L / (4π d²)

  平方反比定律：I = L / (4π d²)

• Parsec definition: distance at which 1 AU subtends 1 arcsecond; d (pc) = 1 / p (arcsec)

  秒差距定义：一天文单位的张角为 1 角秒处的距离；d (pc) = 1 / p (arcsec)

• Apparent magnitude relation: m₂ – m₁ = –2.5 log₁₀(I₂ / I₁)

  视星等关系：m₂ – m₁ = –2.5 log₁₀(I₂ / I₁)

• Absolute magnitude M = m – 5 log₁₀(d / 10 pc)

  绝对星等 M = m – 5 log₁₀(d / 10 pc)

• Wien’s displacement law: λ_max T = constant (2.9 × 10⁻³ m K)

  维恩位移定律：λ_max T = 常数（2.9 × 10⁻³ m K）

• Stefan‑Boltzmann law: L = σ A T⁴ (for a black body, σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴)

  斯特藩‑玻尔兹曼定律：L = σ A T⁴ （黑体，σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴）

• Hubble’s law: v = H₀ d (cosmological redshift z = v / c for v << c)

  哈勃定律：v = H₀ d （宇宙学红移 z = v / c，当 v << c）

• Age of universe estimate: t ≈ 1 / H₀

  宇宙年龄估算：t ≈ 1 / H₀

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