Equation Sheet - Electricity and Magnetism | PHYS 132, Study notes of Physics

Download Equation Sheet - Electricity and Magnetism | PHYS 132 and more Study notes Physics in PDF only on Docsity! Phys 132 Equation Sheet Spring 2009 Electric Forces and Fields: ~E = 1 4π0 q r2 r̂ ~E = 1 4π0 ∑ i qi r2i r̂i ~E = 1 4π0 ∫ dq r2 r̂ ~F0 = q0 ~E ΦE = ∮ ~E · d ~A ΦE = Qencl 0 ~τ = ~p× ~E U = −~p · ~E Infinite sheet: E = σ 20 Electric Potential: V = 1 4π0 q r V = 1 4π0 ∫ dq r U = q0V Vb − Va = − ∫ b a ~E · d~s ~E = −∇V = − ( î ∂V ∂x + ĵ ∂V ∂y + k̂ ∂V ∂z ) Capacitance: Q = CVab C = 0A d 1 Cseries = 1 C1 + 1 C2 + 1 C3 + · · · Cparallel = C1 + C2 + C3 + · · · U = 1 2 QV u = 1 2 0E 2  = K0 Circuits: i = dq dt ∆V = IR i = ∫ ~J · d ~A ~J = ~E ρ = σ ~E R = ρL A Rseries = R1 + R2 + R3 + · · · 1 Rparallel = 1 R1 + 1 R2 + 1 R3 + · · · P = I(∆V ) τ = RC q = Q0e−t/τ q = Q0(1− e−t/τ ) Magnetic Forces and Fields: ~F = q~v× ~B d~F = Id~l× ~B ~τ = ~µ× ~B U = −~µ· ~B µ0Iencl = ∮ ~B · d~s d ~B = µ0 4π Id~s× r̂ r2 Long solenoid: B = µ0nI Long straight wire: B = µ0I 2πr Center of current loop: B = µ0I 2r Induction: ΦB = ∫ ~B · d ~A ε = −dΦB dt ε = vBL ∮ ~E · d~s = −dΦB dt∮ ~B · d~s = µ0 ( ic + 0 dΦE dt ) encl ε = −Ldi dt U = 1 2 LI2 u = B2 2µ0 τ = L R ω = 1√ LC Oscillations and Waves: x = A cos(ωt + φ) ω = 2πf T = 1 f y(x, t) = ym sin(kx− ωt) k = 2π λ v = λf = ω k v = √ FT µ λ = 2L n Electromagnetic Waves: ~F = q( ~E + ~v × ~B) vem = c = 1/ √ 0µ0 E(x, t) = Em sin(kx−ωt) B(x, t) = Bm sin(kx−ωt) k = 2π λ ω = 2πf c = λf E = cB ~S = 1 µ0 ( ~E × ~B) I = Save I = I0 cos2 θ n1 sin θ1 = n2 sin θ2 prad = Save c (totally absorbing) prad = 2Save c (totally reflecting) Interference: φ = 2π λ (r2 − r1) = 2π λ d sin θ d sin θ = mλ d sin θ = ( m + 1 2 ) λ λn = λ n 2nt = mλ 2nt = ( m + 1 2 ) λ I = I0 cos2(φ/2) a sin θ = nλ I = I0 ( sin(β/2) (β/2) )2 β = 2πa λ sin θ 2d sin θ = mλ θR = 1.22λ/d I = I0 cos2(φ/2) ( sin(β/2) (β/2) )2