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Exam2_2010Spr

# Exam2_2010Spr - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2010 Exam Two Equation Sheet Force Law: ( ) ext ext q = + × F E v B r r r r Source Equations: 2 3 1 ˆ 4 4 o o dq dq d r r πε πε = = E r r r r 2 3 ˆ 4 4 o o Id Id d r r μ μ π π × × = = s r s r B r r r r ˆ r r r = r points from source to field point Current Density and Current: open surface I d = ∫∫ J a r r Gauss’s Law: inside closedsurface / o d Q ε = ∫∫ E A r r ± Gauss’s Law for Magnetism: 0 closed surface d = ∫∫ B A r r ± Electric Potential Difference: b b a a V V V d Δ = ≡ − E s r r V = −∇ E r r Potential Energy: U q V Δ = Δ Capacitance: V Q C Δ = 2 2 1 1 2 2 Q U C V C = = Δ Capacitors in Parallel: 1 2 eq C C C = + +⋅⋅⋅ Capacitors in Series: 1 2 1 1 1 eq C C C = + +⋅⋅⋅ Ohm’s Law: V I R Δ = where is the conductivity c c σ σ = J E r r where is the resistivity r r ρ ρ = E J r r Resistors in Parallel: 1 2 1 1 1 eq R R R = + +⋅⋅⋅ Resistors in Series: 1 2 eq R R R = + +⋅⋅⋅ Power Loss in Resistor: 2 2 Joule / P I V I R V R = Δ = = Δ Magnetic Dipole : = I A μ n r ) Torque on Magnetic Dipole: = × τ μ B r r r Constants: 9 2 -2 0 1/ 4 9 10 N m C e k πε = = × 7 -1 0 / 4 10 T m A μ π =

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3 8.02 Exam Two Spring 2010 FAMILY (last) NAME GIVEN (first) NAME Student ID Number Your Section: ____L01 MW 9 am ____L02 MW 11 am ____L03 MW 1 pm ____L04 MW 3 pm ____L05 TTh 9 am ____L06 TTh 11 am ____L07 TTh 1 pm ____L08 TTh 3 pm Your Group (e.g. 10A): ______________ Score Grader Problem 1 (25 points) Problem 2 (25 points) Problem 3 (25 points) Problem 4 (25 points) TOTAL

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