Exam2_2008Spr_Solutions

Exam2_2008Spr_Solutions - MASSACHUSETTS INSTITUTE OF...

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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 Solutions 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) TOTAL
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4 Section I: (25 points) Five Concept Questions. Please circle your answers. Question 1: (5 points) Circle the correct answer. A charged particle is moving in a region of space in which both a non-zero constant electric field and a non-zero constant magnetic field are present. The particle is moving with constant velocity v G throughout the region. Which is true? (a) The electric and magnetic fields are parallel to each other and also parallel to v G . (b) The electric and magnetic fields are parallel to each other and both perpendicular to v G . (c) The electric and magnetic fields are perpendicular to each other and also both perpendicular to v G . (d) The electric field is parallel to v G and the magnetic field is perpendicular to v G . The magnetic force is perpendicular to both the magnetic field and the velocity of the charged particle. Since the electric force must point in the opposite direction of the magnetic force, the electric force and hence the electric field must also be perpendicular to the magnetic field and the velocity of the charged particle.
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5 Question 2: (5 points) Circle the correct answer.
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This note was uploaded on 02/27/2011 for the course PHYSICS 8 taught by Professor Dourmashkin during the Fall '10 term at MIT.

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Exam2_2008Spr_Solutions - MASSACHUSETTS INSTITUTE OF...

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