Exam2_2008Spr

Exam2_2008Spr - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2008 Exam Two Equation Sheet Force Laws: () ext ext q =+ × FEv B GG G G Source Equations: 2 1 ˆ 4 o dq d r πε = Er G 2 ˆ 4 o I d d r µ π × = sr B G G ˆ r r r= G points from source to field point Current Density and Current: open surface I d =⋅ ∫∫ Ja G G Gauss’s Law: inside closedsurface / o dQ ε ⋅= EA G G w Ampere’s Law: closed path open surface o dd Bs v Gauss’s Law for Magnetism: 0 closed surface d BA G G w Electric Potential Difference: b ba a VVV d ∆= − ≡ − ⋅ Es G G Capacitance: V Q C = 2 2 11 22 Q UC V C == Capacitors in Parallel: 12 eq CC C =++ Capacitors in Series: 1 eq C Ohm’s Law: VI R ∆= where is the conductivity cc σσ = JE where is the resistivity rr ρρ = EJ Resistors in Parallel: 1 eq RR R Resistors in Series: eq R Joule Heating: Joule / PI V I R V R =∆ = =∆ Magnetic Dipoles : = I A μ n G ± Torque: = × τ μ B G G G Force: ( / ) zz z Fd B d z = Cross-products of unit vectors : ˆˆ ˆˆˆˆ 0 ×=×= × = ii jjkk ˆˆ ˆ × = i j k ˆ × = j ki ˆ ×= j Kinematics: 2 / cent vr = a G ; / f T ω ππ = = Circumferences, Areas, Volumes: 1) Circle radius r : Area r 2 ; Circumference 2 r 2) Sphere of radius r : Surface Area 4 r 2 ; Volume (4 / 3) r 3 Cylinder of radius r and length l : Area 2 rl ; Volume 2 rl Integrals : dr a b = b a ; 1 ln( / ) b a rd r = 2 (1/ 1/ ) b a r a b =− Constants: 92 - 2 0 1/4 9 10 N m C e k = ⋅ ⋅ 7- 1 0 /4 10 T m A µπ = ⋅⋅
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3 8.02 Exam Two Spring 2008 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 Section 1 (25 points) Problem 1 (25 points) Problem 2 (25 points) Problem 3 (25 points)
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Exam2_2008Spr - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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