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207_FINALkey_spr11

# 207_FINALkey_spr11 - Dr Huerta Phy 207 FINAL ANSWER KEY...

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Dr. Huerta Phy 207 FINAL ANSWER KEY May 10, 2011 Fall 2011, Section HJ, MWF 3:35 – 4:25 p.m. Signature: Name: 1 2 3 4 5 6 ID number: DO PROBLEMS [1.], [2], AND [3.], AND TWO OUT OF PROBLEMS [4], [5.], [6.]. CROSS OUT THE BOX OF THE PROBLEM YOU WILL OMIT Your signature signifies that you will obey the HONOR CODE You may be asked to show your photo ID during the exam. PUT AN X NEXT TO YOUR DISCUSSION SECTION: [ ] Dr. Mezincescu 1O, T 9:30 - 10:20 p.m. [ ] Dr. Alvarez 1Q, T 12:30 - 1:20 p.m. [ ] Dr. Huerta 1R, T 2:00 - 2 :50 p.m. FORMULAE SHEET 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 , ω = p k/m Electric Potential and Energy : W agent i f = ( K + U ) f - ( K + U ) i , W field i f = U i - U f KE = qV acc , U q ( ~ r ) = qV ( ~ r ) , V i - V f = R f i ~ E · d~s, ~ E = - ∂V ∂x ˆ ı - ∂V ∂y ˆ - ∂V ∂z ˆ k, E r = - ∂V ∂r Capacitance Q = CV, U = Q 2 2 C , u E = 0 E 2 2 , C = κ o A d series 1 C eq = 1 C 1 + 1 C 2 , parallel C eq = C 1 + C 2 Circuits i = R ~ J · ˆ n dA, ~ J = q + n + ~v D + + q - n - ~v D - = σ ~ E, σ = 1 /ρ, V = iR, R = ρL/A Resistors : 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. Magnetic forces and Torque : ~ F = q~v × ~ B, ~ F = R i ~ ds × B, ~ τ = μ × ~ B. Physics 207 FINAL May 10, 2011

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Dr. Huerta Phy 207 FINAL ANSWER KEY May 10, 2011 Biot-Savart and Ampere-Maxwell laws : d ~ B = μ 0 i 4 πr 3 d~s × ~ r, B = μ 0 i in 2 πr , I C ~ B · ~ ds = μ 0 i in + μ 0 i D = μ 0 Z S ~ J · ˆ n dA + μ 0 0 Z S ~ E ∂t · ˆ n dA Faraday’s Law : E = - d Φ B dt E = H ( ~ E + ~u × ~ B ) · ~ ds, E = - L d i dt , E 2 = - M di 1 dt Self inductance : E = - L di dt . A coil of length , and cross sectional area A , with n turns per unit length has a self inductance L = μ 0 n 2 ‘A . R-C, or R-L circuits : DC charging capacitor with q ( t = 0) = 0 or inductor with i L ( t = 0) = 0 E applied = q C + i C R, q ( t ) = C E applied (1 - e - t/τ C ) , τ C = RC, i C ( t ) = dq dt or E applied = L di L dt + i L R, i L ( t ) = E applied R (1 - e - t/τ L ) , τ L = L/R. Energy in an inductor : U L = 1 2 Li 2 , the energy density in a B field is u B = B 2 2 μ 0 . Angles : sin π 6 = cos π 3 = 1 2 , cos π 6 = sin π 3 = 3 2 , sin π 4 = cos π 4 = 1 2 Complex numbers : i 2 = e = - 1 , i = e i π 2 , z = x + iy = | z | e , | z | = p x 2 + y 2 , tan θ = y x . AC circuits : In a series R-L-C circuit X L = ωL, X C = 1 ωC , Z = Z R + Z L + Z C , where Z R = R , Z L = iX L , Z C = - iX C , Z = | Z | e , | Z | = p R 2 + ( X L - X C ) 2 , tan φ = X L - X C R , and cos φ = R | Z | .
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