Practice Problem Final Exam_v02_sol.pdf

# Practice Problem Final Exam_v02_sol.pdf - MASSACHUSETTS...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2014 Final Exam Equation Sheet Force Law: F q = q ( E ext + v q × B ext ) Force on Current Carrying Wire: F = Id s × B ext wire Gauss’s Law: E d A closed surface ∫∫ = q enc ε 0 Gauss’s Law for Magnetism: B d A closed surface ∫∫ = 0 Maxwell-Ampere Law: B d s closed path = μ 0 J ˆ n da S ∫∫ + μ 0 ε 0 d dt E ˆ n da S ∫∫ Faraday’s law: E d s closed fixed path = d dt B ˆ n da open surface S ∫∫ Volume Current Density: J = ρ v Surface Current Density: K = σ v Current: I = J ˆ n da open surface ∫∫ Charge Conservation J ˆ n da closed surface ∫∫ = d dt ρ dV volume enclosed ∫∫∫ Volume Energy Density in Fields: 2 1 0 2 E u E ε = ; 2 1 0 2 / B u B μ = Poynting Vector: S = ( E × B ) / μ 0 Source Equations: 3 2 source source ( ) ˆ ( ) e e dq dq k k r = = r r E r r r r B ( r ) = μ o 4 π Id s × ˆ r r 2 source = μ o 4 π Id s × ( r r ) r r 3 source ˆ r points from source to field point Electric Potential Difference: b b a a V V V d Δ = ≡ − E s V = −∇ E Potential Energy: U q V Δ = Δ Capacitance: C = Q Δ V U E = 1 2 Q 2 C = 1 2 C Δ V 2 Inductance: L = Φ B,Total I = N Φ B I back / LdI dt ε = U M = 1 2 LI 2 Electric Dipole: p = q i r i i = 1 N Torque on a Electric Dipole: τ E = p × E ext Magnetic Dipole μ = IA ˆ n RHR

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