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

Download Equation Sheet for Exam Preparation - Electricity and Magnetism | PHYS 132 and more Study notes Physics in PDF only on Docsity! Phys 132 Equation Sheet Fall 2005 Electric Forces and Fields: ~E = 1 4π0 q r2 r̂ ~F0 = q0 ~E ~E = 1 4π0 ∑ i qi r2i r̂i ΦE = ∮ ~E ·d ~A ΦE = Qin 0 ~τ = ~p× ~E U = −~p· ~E Infinite sheet: E = η 20 Electric Potential: V = 1 4π0 q r U = q0V V = 1 4π0 ∑ i qi ri V = 1 4π0 ∫ dq r Vf − Vi = − ∫ f i ~E · d~s Es = − dV ds ~E = −∇V = − ( î ∂V ∂x + ĵ ∂V ∂y + k̂ ∂V ∂z ) Capacitance: C = Q ∆Vc 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 P = I(∆V ) Rseries = R1 + R2 + R3 + · · · 1 Rparallel = 1 R1 + 1 R2 + 1 R3 + · · · τ = RC q = Q0e−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~l × r̂ r2 Long straight wire: B = µ0I 2πr Center of current loop: B = µ0I 2r Long solenoid: B = µ0nI Induction: ΦB = ∫ ~B ·d ~A ε = −dΦB dt ∆VL = −L di dt UL = 1 2 LI2 uB = B2 2µ0 τ = L/R ω = 1√ LC ∮ ~E · d~l = −dΦB dt ∮ ~B · d~l = µ0 ( ic + 0 dΦE dt ) encl Electromagnetic Waves: ~F = q( ~E + ~v × ~B) vem = c = 1/ √ 0µ0 E(x, t) = ĵEmax sin(kx − ωt) B(x, t) = k̂Bmax sin(kx − ωt) k = 2π λ ω = 2πf c = λf E = cB ~S = 1 µ0 ( ~E × ~B) I = I0 cos2 θ AC Circuits: v(t) = V cos(ωt + φ) Vrms = V/ √ 2 XC = 1/ωC XL = ωL Z = √ R2 + (XL −XC)2 Pave = VrmsIrms cos φ Kinematics: v = v0+at x = x0+v0t+ 1 2 at2 v2 = v20 +2a(x−x0) arad = v2 r Vectors: Ax = A cos θ Ay = A sin θ A = √ a2x + A2y ~A · ~B = AB cos φAB ~A · ~B = AxBx + AyBy + AzBz ~A× ~B = n̂AB sinφAB Math: ax2 + bx + c = 0 x = −b± √ b2 − 4ac 2a (1 + x)n ≈ 1 + nx for x  1 Constants: e = 1.602× 10−19 C 0 = 8.85× 10−12 C2/Nm2 µ0 = 4π × 10−7 N/A2 me = 9.109× 10−31 kg c = 3.00× 108 m/s 1