Exam1_2004Fall_Solutions

Exam1_2004Fall_Solutions - Physics 8.02 Exam One Solutions...

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Physics 8.02 Exam One Solutions Fall 2004 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 == Er G r G ˆ points source q observer r r r= from to G 2 0 1 ˆ 4 V dq r = G free, inside closedsurface o Q d κ ε ⋅= ∫∫ EA G G w pointsfrom inside to outside d A G moving from to b ab b a a VV V =−= − ⋅ Es G G d closedpath 0 d G G v point charge 4 o q V r = many point charges 1 4 N i i oi q V = = G K all pairs 0 4 ij U = GG 2 vol 1 2 o UE ⎛⎞ = ⎜⎟ ⎝⎠ ∫∫∫ x d V V =−∇ E G or E x = - V x , E y = - V y , E z = - V z Q C V = 2 2 1 () 22 Q UC V C 1 parallel CC 2 C = + 12 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 Fall 2004 Name_____________________ Problem 1 (25 Points) Circle your choice for the correct answer to the five questions below. A: Consider an electric dipole immersed in a uniform electric field. Which of the following statements regarding the force F G and the torque τ G is strictly true regardless of the orientation of the dipole: 1. and . 0 F G 0 τ G 2. and . 0 = F G 0 τ G 3. and . 0 F G 0 = τ G 4. and . 0 = F G 0 = τ G 5. but may or may not be zero. CORRECT 0 = F G τ G 6. may or may not be zero but F G 0 = τ G . B. Consider the electric field created by an electric dipole. If we observe this dipole from a fixed direction at a distance r much larger than the size of the dipole, the magnitude of the electric field depends on r like E G () Er 1. . ( ) 1/ r 2. 2 () 1 / r 3. . CORRECT 3 / r 4. 4 / r 5. ( ) r 6. 2 r C. Consider a parallel-plate capacitor, where the plates each have an area A . The charges on the plates are + Q and – Q , respectively. What is the magnitude F of the force of attraction between the plates (recall that you can assume that the charge on one plate only feels the electric field created by the charges on the other plate.) 1. 2 0 Q F A ε = . 2. 2 0 2 Q F A = . CORRECT 3. 2 0 2 Q F A = . 4. 2 0 4 Q F A = . Page 2
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8.02 Fall 2004 Name_____________________ D . A rod with charge per unit length λ uniformly distributed over its length is bent into a semicircle of radius . The potential V at the center of the semicircle is a 1. 0
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This homework help was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Fall '07 term at MIT.

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Exam1_2004Fall_Solutions - Physics 8.02 Exam One Solutions...

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