Exam1_2003Fall_Solutions

Exam1_2003Fall_Solutions - Physics 8.02 Exam One Solutions...

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Physics 8.02 Exam One Solutions Fall 2003 PLEASE DETACH THIS SHEET AND USE AT YOUR CONVENIENCE Some (possibly useful) Relations: F = 1 4 πε o q 1 q 2 r 2 23 ˆ 44 oo qq rr == Err G G ˆ points source observer r r r= from to G 2 0 1 ˆ 4 V dq r = Er G inside o closed surface Q ε ⋅= ∫∫ EdA G G w outside to inside from points A d G = = b a a b b to a from moving V V V s d E G G 0 = path closed s d E G G V point charge = q 4 o r = = N i i o i q V 1 4 r r K G charges point many = pairs all j i o j i q q U r r G G 4 2 1 2 ov o l UE d V  =   ∫∫∫ x E x = - V x , E y = - V y , E z = - V z Q C V = U = 1 2 C V 2 = Q 2 2C o parallel plate A C d κε = 12 parallel CC C = + series 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 r 2 Its volume is 3 4 3 r 3) The area of the sides of a cylinder of radius r and height h is 2 r h Its volume is 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 Spring 2003 Name_____________________ Page 2 Problem 1 (25 Points) Circle your choice for the correct answer to the five questions below. A: An electric dipole, consisting of two equal and opposite point charges at the ends of a insulating rod, sits in the electric field of a stationary positive point charge, as shown. The dipole is free to move. The dipole will 1. rotate clockwise and move to the left 2. rotate counterclockwise and move to the right 3. rotate clockwise and move to the right 4. rotate counterclockwise and move to the left CORRECT 5. rotate clockwise but otherwise not move 6. rotate counterclockwise but otherwise not move B: A parallel plate capacitor is connected to a battery and charged to a charge Q . The battery is left in the circuit. A slab of material with dielectric constant κ in inserted between the plates. Which one of the following statements is true? 1. The charge Q on the capacitor plates increases and the voltage difference between the plates increases 2. The charge Q on the capacitor plates decreases and the voltage difference between the plates decreases 3. The charge Q
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Exam1_2003Fall_Solutions - Physics 8.02 Exam One Solutions...

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