PH 132 Exam 1 Spring Student Name. Student Number. Lab/Recitation Section Number (11,,36)

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1 PH 13 Exam 1 Spring 010 Stuent Name Stuent Number ab/ecitation Section Number (11,,36) Instructions: 1. Fill out all of the information requeste above. Write your name on each page.. Clearly inicate your final answers for all multiple-choice questions in the space provie. 3. Present neat an orerly solutions to each problem. Clearly inicate your metho of solution by incluing equations use for each part. Final answers shoul be circle or boxe. 4. Be sure to inclue appropriate units with all answers. 5. Note: The magnitue of the electric fiel at a istance away from the center (an along the central axis) of a thin isk with total charge q an raius is: E q ( ) = k 1 1/ + E q Multiple Choice Problem 1 Problem Total 1

2 Multiple Choice ( pts. each) 1) Two point charges with opposite sign (+nq, -q) resie on the positive x-axis at positions x = an x =, respectively. A thir point charge (+Q) is locate at position x = 3 where it resies in electrostatic equilibrium. Consequently, 0 +nq -q +Q 3 x A) n = 4; B) n = 9; C) n = 16; D) n = 5. Answer ) A negatively charge ball is brought close to (but oes not touch) the right sie of a neutral isolate conucting sphere. The conucting sphere is then groune on the left sie while the ball is kept close. The groun connection is remove an the ball is taken away, leaving the conucting sphere: A) positively charge via the process of conuction; B) negatively charge via the process of conuction; C) positively charge via the process of inuction; D) negatively charge via the process of inuction. Answer 3) At large istances () away from which charge istribution oes the electric fiel resemble the fiel of a single point charge? A) Two point charges of equal magnitue an like sign separate by a small istance ; B) Two point charges of equal magnitue an unlike sign separate by a small istance ; C) An infinite nonconucting line of charge with linear charge ensity λ; D) An infinite nonconucting sheet of charge with uniform charge ensity σ; Answer

3 4) Four ientical point charges (+q) are locate at the corners of a square of sie. The square resies in a plane perpenicular to the -axis an its center point coincies with the origin. v 4 k q The electric fiel at any point on the -axis is given by: E = kˆ. 3 / + ( / ) ( ) At small istances (near fiel region) from this charge istribution, the magnitue of the electric fiel is approximately equal to: 4 k q A) ; 4k q B) ; 3 8 k q C) ; D) 8 k q. Answer 3 5) A plot of the electric fiel given in the previous problem is shown below. At what location on the -axis is the electric fiel maximum? E() A) B) C) D) = ; = ; = ; =. Answer 4 3

4 6) Consier two ientical nonconucting ros carrying equal uniformly istribute charges with opposite signs, as shown. What is the irection of the net electric fiel at the origin? y x A) positive x-irection; B) negative x-irection; C) positive y-irection; D) negative y-irection. Answer 7) After being tosse into a ryer full of wool blankets for an entire cycle on Delicate, Dr. Jim emerges with a net negative charge. Before he can share his charge with me, I manage to safely isolate an enclose him in a Gaussian sphere. I measure the electric flux he prouces to be N m /C an estimate that he has been charge with an excess of A) 10 electrons; B) electrons; C) electrons; D) electrons; E) electrons. Answer 8) A positive point charge (+q) is place at a istance away from the insie wall of a thin spherical nonconucting shell of positive charge (+Q) an raius (as shown). The magnitue of the force acting on the point charge is equal to: +Q +q A) 0; B) k ; C) k ; D) k ; E) k ( ). Answer 4

5 9) A positive point charge (+q) is place at a istance away from the outsie wall of a thin spherical nonconucting shell of positive charge (+Q) an raius (as shown). The magnitue of the force acting on the point charge is equal to: +Q +q A) 0; B) k ; C) k ; D) k ; E) k + ( ). Answer 10) A thick spherical copper shell has an outer raius of an an inner raius of. The amount of charge resiing on the shell s inner surface is 5µC an on the outer surface is 15µC. At the center of the copper shell, an concentric with it, is a: A) 15µC point charge; B) + 15µC point charge; C) 5µC point charge; D) + 5µC point charge; E) 40µC point charge; F) + 40µC point charge. Answer 5

6 Problem 1 A nonconucting cylinrical volume of raius an length carries a uniformly istribute total charge of +q. The bottom of the cyliner resies in the xy plane with center locate at the origin. q y x a) Using the expression for the electric fiel of a isk of charge (see cover page), fin an expression v for the electric fiel E prouce at the origin for this cyliner of charge. Your solution must inclue an illustration ocumenting your approach with all variables that you use clearly labele. You shoul use the picture above for this purpose. (1 pts.) b) Fin the force on a positive point charge +q locate at the origin. (3 pts.) c) At what istance irectly below the origin coul you locate this positive point charge +q to make the electric fiel at the origin vanish? Assume that = = 1.0 m. (5 pts.) 6

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8 BONUS: Proceeing from part a): A smaller charge cyliner of raius r an length l, with a uniformly istribute charge of + Q, is place below the original cyliner in such a way that the ens meet (top of small cyliner is flush with bottom of original cyliner) an are centere at the origin. Fin a simple expression for Q in terms of q that will insure the electric fiel at the origin will vanish. For simplicity, assume that r = / an l = /. (3 pts.) 8

9 Problem Consier two concentric nonconucting thin spherical shells of charge. The inner sphere has a raius a an a positive uniform surface charge ensity + σ. The outer sphere has a raius 3 a an a negative uniform surface charge ensity σ / 3. Use Gauss aw to obtain an expression for the magnitue of the electric fiel σ/3 +σ a a a b b 3 a E a) E I in the region b) E II in the region E in the region > 3 a c) III r < a ; (5 pts.) a < r < 3 a ; (5 pts.) r. (5 pts.) 0 a ) Plot the magnitue of the electric fiel in the raial irection on the graph given. Be sure to label the actual magnitue of the fiel at r = a an r = 3 a. (5 pts.) BONUS: You wish to make the electric fiel between the two spherical shells vanish. To accomplish this, you place a negative point charge (-q) at the center of the smallest shell ( r = 0 ). Fin an expression for the magnitue of this point charge. (3 pts.) 3 a r 9

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