AP Physics C E&M Summary Sheet

作者: AnonTokyo

简介: AP物理C电磁常用公式一览

最后修改: 2025-04-27 16:53:09.015095

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Ph ysics C EM S ummary Sheet F ebruary 16, 2025 1 Electric Charge, Electric Field, and Electric P oten tial • Charge Prop erties : Lik e c h arges rep el, opp osite c harges attract; Conserv ed and quan tized in in teger m ultiples of elemen tary c harge • Coulom b’s La w : F = 1 4 π ε 0 q 1 q 2 r 2 ˆ r • Electric Field : E = F q 0 (Unit: N/C or V/m) • P oin t Charge Field : E = 1 4 π ε 0 Q r 2 ˆ r • Electric P oten tia l E nergy : U = q V ; Electric P oten tial : V = U q (Unit: V olt ) • Field-P oten tial Relationship: V B − V A = − R B A E · d l 2 Electric Flux and Gauss’s La w • Electric Flux : Φ E = R R E · d A • Gauss’s La w : Φ E = Q enc ε 0 • Key Applications: – Uniformly c harged sphere: E = Q 4 π ε 0 r 2 ( r ≥ R ) – Innite straigh t wire: E = λ 2 π ε 0 r – Innite c harged plane: E = σ 2 ε 0 3 Capacitors • Capacitance Denition : C = Q V (Unit: F arad) • P arallel-plate capacitor: C = ε 0 A d • Energy storage: U = 1 2 C V 2 = Q 2 2 C • Series com bination: 1 C eq = P 1 C i • P arallel com bination: C eq = P C i 1
4 Resistance and DC Circuits • Resistivit y : R = ρ L A ( ρ = resistivit y) • Ohm’s La w : V = I R • Kirc hho ’s La ws : – Junction Rule: P I in = P I out – Lo op Rule: P ε = P I R • R C Circuits : – Charging: Q ( t ) = Q max (1 − e − t/R C ) – Disc harging: Q ( t ) = Q 0 e − t/R C 5 Magnetism and Magnetic Fields • Loren tz F orce : F = q ( E + v × B ) • Biot-Sa v art La w : d B = µ 0 4 π I d l × ˆ r r 2 • Amp ` e r e ’s Circuital La w : I B · d l = µ 0 I enc • Long straigh t wire: B = µ 0 I 2 π r • Solenoid eld: B = µ 0 nI 6 Electromagnetic Induction • F arada y’s La w : E = − d Φ B dt • Lenz’s La w : Induced curren t opp oses ux c hange 7 Maxw ell’s Equations In tegral F orm: I E · d A = Q enc ε 0 (Gauss’s La w) I B · d A = 0 (Gauss’s La w f or Magnetism) I E · d l = − d dt Z B · d A (F arada y’s La w) I B · d l = µ 0 I enc + µ 0 ε 0 d dt Z E · d A (Amp ` ere-Maxw ell La w) With Constitutiv e Relations : D = ε E , B = µ H , J = σ E 2
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