Exam I solutions - PH 132 Exam 1 Spring 2005 Student Name...

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Unformatted text preview: PH 132 Exam 1 Spring 2005 Student Name __ we 7‘} {53’ 5‘33 g Student Number in Labeecitation Section Number - (11,...,34) Instructions: 1. Fill out all of the information requested above. Write your name on each page. 2. Clearly'indicate your final answers for all multiple-choice questions in the space provided. 3. Present neat and orderly solutions to each problem. Clearly indicate your method of solution by including equations used for each part. Final answors should be circled or boxed. 4. Be sure to include appropriate units with all answers. 5. The magnitude ofthe electric field at a distance 1‘ above the midpoint ofa finite line of total charge + q and length L is: 2kg YO? +4r2)% E: Multiple Choice Problem 1 Problem 2 Total Multiple Choice (2 pts. each) 1) 2) 3) 4) Two point charges gI-(positive) and g2 (negative) are separated by a distance d. A third point charge Q (negative) is located a distance (1/2 to the left of the first charge, as shown. l f the net electrostatic force on the third charge is zero, then the magnitudes of the first two charges must be related according to: A) 92 2 29‘}: \k B) q :39? , -——-—-- :: .__..._....... c) q: = 4931, \ (5%): A D nswer_m_____w D) 92:997y 5:51 A positiver charged ball is brought close to (but does not touch) the left side of a neutral isolated conducting Sphere. The conducting sphere is then grounded on the right side while the ball is kept close. The ground connection is removed and the ball is taken away, leaving the conducting sphere: £9 Answer A) Positively charged via the process of conduction; B) Negatively charged via the process of conduction; C) Positively charged via the process of induction; D) Negatively charged via the process of induction. Consider the electrical; effect ofa dipole at a distance that is large compared with the size ofthe dipole. If you double this distance from the dipole, the strength of the electric field is reduced by a factor of: - l A) 1:2; ‘5“ r3 C) 1E6; --*' D) U8. Answer b Consider the finite line of positive charge q and length L on the cover page. The magnitude of 2kg r052 +4r2y/2- Rcspectively, the magnitude of E in the near field (at distances close to the line) and in thefar field (at distances far from the line) is proportional to: the electric field at any distance 1‘ above the midpoint is given by: E = z 2.. '2- ...—- H k1: ‘lr’ :2; r- «PA: “a: — l A) L and M L + q kw”... r r I 1 z 7. 3’- zJai if" I ‘3‘ B ~— d——, wwL-I-HF’A'LA-V a: '5 ---‘ ) r an r2 FA); (F?) L.) E m4 C) l; and -1~; r r D) if and Answermem r r 5) Consider a finite nonc‘onducting rod with uniformly distributed positive charge (+Q) along the positive yards and uniformly distributed negative charge (-Q) along the negative y-axis. Each piece ofthe road has the same length. What is the direction ofthe electric field at point P? ® A) positive x direction; B) negative x direction; C) positive y direction; D D) negative y direction. Answer_ 6) A point charge (+10q) is iocated at the Center of the flat face of a hemiSphere of radius R. What is the net electric flux through the curved surface of this hemisphere? A) i; 60 B) 3'1; 80 C) 192; 80 n J 7) A negative point charge (-q) is placed at a distance d away from the inside wall of a thin spherical shell of positive charge (+Q) and radius R. The magnitude of the force acting on the point charge is equal to: E) km—(fn—QE-fu. AHSWer" Z S 8) A 2.0 g particle carrying a charge of 2.0 ,uC is released from rest in a uniform electric field of strength 500 MC. How far will this particle travel in 4.0 5? ‘u—.____‘be nub A) 2.0 m; «fin E B) 4.0m; C) 8.0 m; D) 16 m. Answer 9) The figure below shows two large, parallel, nonconducting sheets with identical (positive) uniform surface charge densities, and a positive point charge. You move the point charge to each of the four positions shown. Rank the positions according to the magnitude of the net force experienced by the charge, greatest first? “:3 c“ I; i: genwfi' ‘- 2-50 :5 -" 0‘ 1‘ mate-7’ 41‘ "‘ "2-5. gun—HI "fl 2* . u a 5: 0 fi- M ‘7" A a... /“ = Z Ema: T‘ = o A) 1 and 2 are tied, followed by 3, then 4; B) l and 2 are tied, fol10wed by 4, then 3; C) 1, 2 and 4 are tied, followed by 3; D) 3 and 4 are tied, followed by l and 2 (which are tied); E E) all are the same. Answer 10) A ball of charge —50e'resides at the center ofa hollow spherical metal shell that has a net charge of ~100e. What is the charge on the Shell’s outer surface? A) +50e; B) +100e; C) ~50e; D) -150e. AnswerL Problem I A thin noncondocting half cylinder of radius R and length L carries a uniformly distributed total charge of ~+~q. Z 3) Using the expression for the electric field of a line of charge (see cover page), find an expression for the electric field E at the origin (mid-point) for this half cylinder. Your solution must include an illustration documenting your approach with all variables that you use clearly labeled. You should use the line of charge in the picture above for this purpose. (14 pts.) 1}) Find the force on a positive point charge +q located at the origin. (3 pts.) c) At what location on the z—axis could you locate this positive point charge to make the electric field at the origin vanish? Assume that R = 1.0 m and L = 2.0 m. (3 pts.) §_QNUS: Consider the magnitude of the electric field at the origin, if instead this were a quarter cylinder. What is the coefficient C in the following expression: E 5:. cylinder = CE y: cylinder ‘2 (3 pts.) . M, """"""""""" "”““‘"-~._._:_\ “HM-I‘M" ? .— i A a. 2 I . W: EEI = lass—©- 0' == = . jam (LL-r as )‘éfl arm. U235 . . ass. 5" :2 Glue y ammo-5. enema-EL aw-m-w’s. Rob __, __ Lid-Masha "‘ A; " + SUM '. _ 1L 5 flag" 2%? ago a" gun. at (Ltltqkzyé -3154- “ :memmmmx L3__g—l 3'1 -_ LI; <5 " mg, (sz22}?- 6 We WM”. seats é/MJTfi of: mTé'éRA‘riom Problem 2 Consider an infinitely long nonconducting solid cylinder of uniform volume charge density + ,0 whose core has been removed. The remaining solid portion ofthe cylinder has an inner radius a. and outer radius b. Use Gauss’ Law to obtain an expression for the magnitude of the electric field E Em N J, K " I" 0 a b MUTE: AT- Fab Top _ f has? i a“""2£.< b ) Side View a) ElF in the region I” < a . (5 pts.) b) E” in the region a < r < b. (5 pts.) c) Em in the region r > b. (5 pts.) (1) Plot the magnitude of the electric field in the radial direction on the graph given. Be sure to label the actual magnitude of the field at r :0, a, and b . (5 pts.) BONUS: Consider a case where the core is filled with a material having a uniformly distributed negative charge (— p' ). Find ' in terms of _: ifthe electric field in the region r > b is zero. (3 pts.) use" A Gsoeemw ‘ mew—e weak or? my“; r“ mar) macaw-l It germ EMA fleas; and. 42:11” + gm: Barr 51b: 3 o n —— -----3’§-°--_m3-_-_u ‘W ...
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This note was uploaded on 11/04/2009 for the course PHYSICS 131 taught by Professor Wick during the Spring '08 term at Clarkson University .

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Exam I solutions - PH 132 Exam 1 Spring 2005 Student Name...

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