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Exam1_2002Fall_Solutions

# Exam1_2002Fall_Solutions - Physics 8.02 Exam One Fall 2002...

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Physics 8.02 Exam One Fall 2002 PLEASE DETACH THIS SHEET AND USE AT YOUR CONVENIENCE Some (possibly useful) Relations: F = 1 4 πε o q 1 q 2 r 2 E = q 4 πε o r 2 ˆ r observer to source from points r ˆ 2 0 1 ˆ 4 V dq r πε = E r G = surface closed o inside Q ε dA E outside to inside from points dA = = b a a b b to a from moving V V V ds E 0 = path closed ds E V point charge = q 4 πε o r = = N i i o i q V 1 4 r r πε charges point many j i q q U i j j i o j i = ∑∑ , 4 2 1 r r πε E x = - V x , E y = - V y , E z = - V z C Q V U = 1 2 C V 2 = Q 2 2C d A o plate parallel ε κ = C Circumferences, Areas, Volumes: 1) The area of a circle of radius r is π r 2 Its circumference is 2 π r 2) The surface area of a sphere of radius r is 4 π r 2 Its volume is 3 3 4 r π 3) The area of the sides of a cylinder of radius r and height h is 2 π rh Its volume is π r 2 h Definition of trig functions sin is opposite/hypotenuse; cos is adjacent/hypotenuse; tangent is opposite over adjacent; Properties of 30, 45, and 60 degrees ( π /6, π /4, and π /3 radians) : sin( π /6) = cos( π /3) = 1/2, sin( π /3) = cos( π /6) = 2 / 3 ; sin( π /4) = cos( π /4) = 2 / 1 ; Integrals that may be useful a b dr b a = ) / ln( 1 a b dr r b a = = b a dr r b a 1 1 1 2

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8.02 Fall 2002 Name_____________________ Page 2 Part I - Concept Questions (25 Points) Circle your choice for the correct answer to the five concept questions below. Each question is worth five points. A: An electric dipole, consisting of two equal and opposite point charges at the ends of a insulating rod, is free to rotate about a pivot point in the center. The rod is placed in a non-uniform electric field. The dipole will experience 1. a noticeable electric force and no noticeable electric torque 2. no noticeable electric force and a noticeable electric torque 3. a noticeable electric force and a noticeable electric torque CORRECT 4. no noticeable electric force and no noticeable electric torque B: When you place a positively charged particle in an electric field, does it move from 1. higher to lower electric potential and lower to higher potential energy 2. higher to lower electric potential and higher to lower potential energy CORRECT 3. lower to higher electric potential and lower to higher potential energy 4.
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