207_test2_formula_sheet_fall11

207_test2_formula_sheet_fall11 - 2 Electric current i = R ~...

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FORMULAE SHEET TEST II Z dx x 2 + a 2 = ln( x + p x 2 + a 2 ) , Z xdx ( x 2 + a 2 ) 3 / 2 = - 1 ( x 2 + a 2 ) 1 / 2 , Z dx ( x 2 + a 2 ) 3 / 2 = x a 2 ( x 2 + a 2 ) 1 / 2 e = 1 . 6 × 10 - 19 C, m e = 9 . 1 × 10 - 31 kg, m p = 1 . 67 × 10 - 27 kg, k = 1 4 π± 0 = 9 × 10 9 N · m 2 C 2 . Coulomb’s Law, Electric Fields (N/C), Electric Field Flux Φ , and Gauss’ Law ± ± ~ F ± ± = ± ± q 1 q 2 ± ± 4 π± 0 r 2 ~ F q = q ~ E, | ~ E Q | = kQ r 2 , Φ closed surface = H ~ E · d ~ A = q inside ± 0 Electric Field and sheets of surface charge density σ : On each side of an infinite sheet E n = σ 2 ± 0 . However, outside the surface of a conductor, E n = σ ± 0 . Force, Potential Energy and Torque for an Electric Dipole The Force, torque, and potential energy of an electric dipole ~ p immersed in uniform electric field ~ E are ~ F total = 0 , U = - ~ p · ~ E, ~ τ = ~ p × ~ E. Harmonic Oscillator: F x = - kx , d 2 x dt 2 + ω 2 x = 0 , ω = p k/m Electric Potential and Energy : W agent = ( K + U ) f - ( K + U ) i , W field = U i - U f U q ( ~ r ) = qV ( ~ r ) , V i - V f = R f i ~ E · d~s, ~ E = - ~ V = - ∂V ∂x ˆ ı - ∂V ∂y ˆ - ∂V ∂z ˆ k, E r = - ∂V ∂r Capacitance Q = CV, C = κ± o A d , series 1 C eq = 1 C 1 + 1 C 2 , parallel C eq = C 1 + C
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Unformatted text preview: 2 Electric current i = R ~ J · ˆ ndA, ~ J = q + n + v D + + q-n-v D-= σ ~ E, σ = 1 /ρ , ρ = m ne 2 τ Resistance : V = iR, R = ρL A , in series R eq = R 1 + R 2 , in parallel 1 R eq = 1 R 1 + 1 R 2 Kirchhoff’s rules : (1) at a junction, current in equals current out, (2) sum of voltage rises around a loop equals zero. RC Circuits : E , switch, R , and C in series. Charge in capacitor q ( t ) , q ( t ) = C E ² 1-e-t/τ ³ + q ( t = 0) e-t/τ , τ = RC, i ( t ) = dq dt Magnetic fields and forces : I ~ B · d ~ A = 0 , F = q~v × ~ B, ~ F = Z i ~ ds × B, ~μ = IA ˆ n, ~ τ = μ × ~ B....
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This note was uploaded on 01/08/2012 for the course PHYSICS 207 taught by Professor Huerta during the Fall '11 term at University of Miami.

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