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em equations sheet - Physics 2220.003 Spring 2007 Final...

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Physics 2220.003 Spring 2007 Final Exam Equation Sheet F 12 electric = k e q 1 q 2 r 2 ˆ r E F electric q 0 E = k e i q i r 2 i ˆ r i E = k e dq r 2 ˆ r r = r 0 + v 0 t + 1 2 at 2 v = v 0 + at a c = v 2 r Φ electric = E · dA E · dA = q enclosed 0 Δ V Δ U q 0 = B A E · ds V = k e i q i r i V = k e dq r U = k e unique pairs q i q j r ij E = V ≡ − ∂V ∂x ˆ i ∂V ∂y ˆ j ∂V ∂z ˆ k C Q Δ V C parallel equiv . = i C i 1 C series equiv . = i 1 C i U = Q 2 2 C = 1 2 Q Δ V = 1 2 C V ) 2 u E = 1 2 0 E 2 C = κC 0 C plate = 0 A d Electric dipole : p d · q τ = p × E U = p · E Magnetic dipole : μ = IA τ = μ × B U = μ · B I dQ dt I avg . = nqv d A = JA J = σE R Δ V I R = ρ l A P = I Δ V = I 2 R = V ) 2 R R series equiv . = i R i 1 R parallel equiv . = i 1 R i I in = I out closed loop Δ V = 0 Y = Y 0 e t/τ Y = Y 0 (1 e t/τ ) τ = RC or τ = L/R Y ∈ { V, Q, I } F Lorentz = q ( E + v × B ) F = IL × B dB = μ 0 4 π I ds × ˆ r r 2 F B l = μ 0 I 1 I 2 2 πa B solenoid = μ 0 N l I B straight wire = μ 0 I 4 πa (cos θ 1 cos θ 2 ) B · ds = μ 0 I + μ 0 0 d Φ E dt Φ B = B · dA B · dA = 0 E = E · ds = d Φ B dt E L = L dI dt L = N Φ B I E 2 = M 12 dI 1 dt M 12 = N 2 Φ 12 I 1 = M 21 = M
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U = 1 2 LI 2 u B = B 2 2 μ 0 ω = 1 LC Y rms = Y max 2 X L ωL X C 1 ωC Z R 2 + ( X L X C ) 2 φ = arctan( X L X C R ) I rms = Δ V rms Z P avg = I rms Δ V rms cos φ = I 2 rms R Δ V 2 = N 2 N 1 Δ V 1 I 1 Δ V 1 = I 2 Δ V 2 E B = c S 1 μ 0 E × B P = S c or 2 S c c = λf I = S avg . I = P 4 πr 2 θ 1 = θ
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