Equation Sheet 3

Equation Sheet 3 - Physics 2220.003 Spring 2007 Exam III...

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Physics 2220.003 Spring 2007 Exam III Equation Sheet ~ F 12 electric = k e q 1 q 2 r 2 ˆ r ~ E ~ F electric q 0 ~ E = k e X i q i r 2 i ˆ r i ~ E = k e Z dq r 2 ˆ r ~r = 0 + ~v 0 t + 1 2 ~at 2 = 0 + a c = v 2 r Φ electric = Z ~ E · d ~ A I ~ E · d ~ A = q enclosed ± 0 Δ V Δ U q 0 = Z B A ~ E · d~ sV = k e X i q i r i V = k e Z dq r U = k e X unique pairs q i q j r ij ~ E = ~ 5 V ≡− ∂V ∂x ˆ i ∂y ˆ j ∂z ˆ k C Q Δ V C parallel equiv . = X i C i 1 C series equiv . = X 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 k plate = ± 0 A d Electric dipole : p d · q~ τ = ~p × ~ EU = · ~ E Magnetic dipole : μ = IA = × ~ BU = · ~ B I dQ dt I avg . = nqv d A = JA ~ J = σ ~ E R Δ V I R = ρ l A P = I Δ V = I 2 R = V ) 2 R R series equiv . = X i R i 1 R parallel equiv . = X i 1 R i X I in = X I out X 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 + × ~ B ) ~ F = I ~ L 0 × ~ Bd ~ B = μ 0 4 π Id~s × ˆ r r 2 F B l = μ 0 I 1 I 2 2 πa B solenoid = μ 0 N l IB straight wire = μ 0 I 4 (cos θ 1 cos θ 2 ) I ~ B · d~s = μ 0 I + μ 0 ± 0 d Φ E dt Φ B = Z ~ B · d ~ A I ~ B · d ~ A E = I ~ E · = 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 p R 2 +( X L X C ) 2 φ =arctan( X L X C R ) I rms = Δ V rms Z P avg = I rms
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Equation Sheet 3 - Physics 2220.003 Spring 2007 Exam III...

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