Download Formula sheet physics 208 and more Cheat Sheet Physics in PDF only on Docsity! PHYSICS 208 EXAM II Formula/Information Sheet • Basic constants: Gravitational acceleration on Earth’s surface g = 9.8 m/sec2 Permittivity of free space ε0 = 8.8542× 10−12 C2/N·m2 [ k = 1/4πε0 = 8.9875× 109 N·m2/C2] Permeability of free space µ0 = 4π × 10−7 T·m/A [ km = µ0/4π = 10−7 Wb/A·m] Elementary charge e = 1.60× 10−19 C Unit of energy: electron volt 1 eV = 1.60× 10−19 J Unit of energy: kilowatt-hour 1 kWh = 3.6× 106 J • Properties of some particles: Particle Mass [kg] Charge [C] Proton 1.67× 10−27 +1.60× 10−19 Electron 9.11× 10−31 −1.60× 10−19 Neutron 1.67× 10−27 0 • Some indefinite integrals: ∫ dx x = ln x ∫ dx a+bx = 1 b ln (a+ bx)∫ dx (x2+a2)3/2 = x a2 √ x2+a2 ∫ x dx (x2+a2)3/2 = − 1√ x2+a2∫ dx√ x2±a2 = ln (x+ √ x2 ± a2) ∫ x dx√ x2±a2 = √ x2 ± a2 Coulomb’s law (q at ~r1, q′ at ~r2) | ~F | = k |q1q2| |~r2 − ~r1|2 Electric field [N/C = V/m] (q at ~r′, observer at ~r, ~R ≡ ~r′ − ~r) ~E(~r) = k q R2 R̂ (group of charges) ~E = ∑ ~Ei = ∑ kqi R2 i R̂i (continuous charge distribution) ~E = ∫ d ~Ei = ∫ kdq R2 R̂ line charge λ | ~E| = 2k|λ| r sheet charge σ | ~E| = 2πk|σ| Electric force [N] (on q subject to ~E) ~F = q ~E Electric flux (small area ∆Ai, outward normal n̂i) ∆ΦE = ~Ei · n̂i∆Ai = Ei ∆Ai cos θi (through an entire surface area) ΦE = lim ∆A→0 ∑ ∆ΦE = ∫ dΦE = ∫ ~E · n̂dA Gauss’ law (through a closed surface area) ΦE ≡ ∮ dΦE = ∮ ~E · n̂dA = 4πkQenc Conductor ( ~E · n̂)out = 4πkσS Electric potential [Volt = J/C] (definition, step-length ds along ŝ) ∆V = VB − VA = ∫ B A dV = − ∫ B A ~E · ŝds ( ~E = constant) ∆V = − ~E · (~rB − ~rA) (point charge q at ~r′) V (~r) = k q |~R| (V (∞) = 0) (group of charges, ~Ri ≡ ~r − ~ri) V (~r) = ∑ Vi(|~Ri|) = ∑ kqi |~Ri| (V (∞) = 0) (continuous charge distribution) V (~r) = ∫ dV = ∫ kdq |~R| (V (∞) = 0) Electric potential energy [J] (definition) ∆U = UB − UA = −q0 ∫ B A ~E · ŝds = q0 (VB − VA) ~E from V ~E = −~∇V (~∇ = gradient operator) Electric potential energy of two-charge system U12 = k q1q2 |~r1 − ~r2|
