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Ex2_Sp06

# Ex2_Sp06 - Physics 241 Exam#2 This exam consists of 13...

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Physics 241 – Exam #2 March 30 2006 This exam consists of 13 problems on 9 pages. Please check that you have them all. Each problem is worth 12 points unless otherwise noted. All of the formulas that you will need are given below. You may also use a calculator. sin θ = y/r cos θ = x/r tan θ = y/x x y r θ e = 1 . 6 × 10 - 19 C k = 9 . 0 × 10 9 N · m 2 / C 2 epsilon1 0 = 8 . 9 × 10 - 12 C 2 / (N · m 2 ) F = kq 1 q 2 r 2 = q 1 q 2 4 πepsilon1 0 r 2 E = kq r 2 Φ = integraldisplay vector E · vector dA = q epsilon1 0 charged plane : E = σ 2 epsilon1 0 V = U E q = - integraldisplay vector E · vector dl dV = - vector E · vector dl point charge : V = kq r U E = q 0 V = kqq 0 r E x = - ∂V ∂x 1 Volt = 1 J / C 1 Volt / m = 1 N / C U E = 1 2 qV C = q V Surface area(sphere) = 4 πR 2 capacitor : U E = 1 2 q 2 C = 1 2 qV = 1 2 CV 2 u E = 1 2 epsilon1 0 E 2 parallel plate capacitor : C = epsilon1 0 A d isolated spherical capacitor : C = 4 πepsilon1 0 R capacitors in parallel : C = C 1 + C 2 + C 3 ... capacitors in series : 1 C = 1 C 1 + 1 C 2 + 1 C 3 ... C = κC 0 I = q t R = V I R = ρ L A V = IR 1

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P = IV = I 2 R = V 2 R P = E I resistors in series : R = R 1 + R 2 + R 3 ... resistors in parallel : 1 R = 1 R 1 + 1 R 2 + 1 R 3 ... q ( t ) = q 0 e - t/ ( RC ) = q 0 e - t/τ I ( t ) = V R e - t/ ( RC ) = I 0 e - t/τ τ = RC q ( t ) = C E (1 - e - t/ ( RC ) ) = q 0 (1 - e - t/τ ) I ( t ) = E R e - t/ ( RC ) = I 0 e - t/τ vector F B = qvectorv × vector B vector F B = I vector L × vector B vector B = μ 0 4 π qvectorv × ˆ r r 2 Φ B = BA cos θ μ 0 = 4 π × 10 - 7 T · m / A d vector B = μ 0 4 π Id vector lscript × ˆ r r 2 integraldisplay vector B · d vector lscript = μ 0 I B (center of circular loop) = μ 0 I 2 R B (wire) = μ 0 I/ (2 πr ) B (solenoid) = μ 0 nI E = - d Φ B dt U L = 1 2 LI 2 V L = - L dI dt L = μ 0 n 2 Alscript U B = 1 2 μ 0 B 2 ( V ol ) u B = 1 2 μ 0 B 2 I = V R (1 - e ( - t/τ ) ) | V L | = V e ( - t/τ ) τ = L/R ω = 2 πf X C = 1 ωC X L = ωL ω
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