Exam Total /200 PHYS 2135 Exam I Febuay 13, 2018 Name: Recitation Section: Five multiple choice questions, 8 points each Choose the best o most nealy coect answe Fo questions 6-9, solutions must begin with a coect OSE You must show wok to eceive full cedit fo you answes Calculatos ae NOT allowed (8) A 1 The figue illustates the electic field in a P 1 egion E i efes to the magnitude of the electic field at the location, P i Which of the following is tue? [A] E 1 < E 2 [B] E 1 E 2 P 2 [C] E 1 > E 2 [D] The elative magnitudes of E 1 and E 2 cannot be detemined E (8) C 2 If an electon wee placed at each of the positions in the pevious figue, and if U i denotes the potential enegy of the electon when it is at point P i, which of the following is tue? [A] U 1 < U 2 [B] U 1 U 2 [C] U 1 > U 2 [D] The elative values of the two enegies cannot be detemined (8) B 3 The figue shows an electic dipole moment oiented anti-paallel to a unifom electic field Fo this oientation, the toque on the dipole is and the potential enegy of the dipole is [A] 0, minimum [B] 0, maximum [C] minimum, 0 [D] maximum, 0 (8) C 4 A chage inside a Gaussian suface of aea A geneates an electic flux though the suface If the magnitude of the chage is halved and the aea A is doubled, what is the new electic flux though the suface? [A] [B] 2 [C] /2 [D] 4 (8) 5 The best featue of an anti-paallel univese is that [A] the sun absobs light [B] potons obit aound electons [C] electic fields ceate chages [D] faculty take tests witten by students
6 In the diagam at ight, a positive point chage, o, lies at y the oigin, a positive point chage, 1, lies at the point (0,h) w and a negative point chage 2 lies at the point (w,h) 1 2 Expess you answes symbolically and in unit vecto notation 2 1 h (10) (a) Calculate the electic field at the oigin due to 1 o Ek q 2 x E 1 k 1 h 2 ĵ (10) (b) Calculate the electic field at the oigin due to 2 2 w î h ĵ w 2 +h 2 w w 2 +h î 2 h w 2 +h 2 ĵ 2 2( w E 2 k w 2 +h w 2 +h î 2 E 2 k h w 2 +h ) ĵ 2 2 (w 2 +h 2 ( w î h ĵ ) 3/ 2 ) (10) (c) Calculate the net electic field at the oigin due to 1 and 2 E T E 1 + E 2 E T k w 2 (w 2 +h 2 ) 3 /2 î k ( 1 h 2 + h 2 (w 2 +h 2 ) 3/2) ĵ (10) (d) Calculate the net electic foce on o F q E F k o w 2 (w 2 +h 2 ) 3 /2 î k o( 1 h 2 + h 2 (w 2 +h 2 ) 3/2) ĵ
7 A thin insulating thee-quate cicle of adius, R, y is held fixed in the xy-plane with its cente at the oigin of the coodinate system, as shown It caies a negative chage of -3 unifomly distibuted ove its length An electon is eleased fom est at the oigin θ (25) (a) Find the initial acceleation of the electon in tems of the system paametes x Expess you answe in unit vecto notation R (Gavity may be neglected) R cosθ î R sinθ ĵ R cos θ î sinθ ĵ λ 3 2 3 2 π R π R dqλ Rdθ 2 π d θ F a m 1 m k q 1dq 2 2 a k m π/2 ( e)( 2 π d θ) π R 2 ( cosθ î sinθ ĵ) 2ke π/2 a m π R 2 π d θ(cosθ î +sinθ) a 2ke m π R [sinθ î 2 cosθ ĵ ] π/2 π a 2ke m π R 2 [(1 0)î (0+1) ĵ ] a 2ke m π R 2 ( î + ĵ ) (15) (b) Detemine the maximum speed the electon eaches in tems of the system paametes U o +K o U f +K f k ( e)( 3 ) 1 R 2 mv2 6ke mr v whee, U f 1 0 K o 0
8 A solid insulating sphee of adius, a, has a total positive chage,, unifomly distibuted thoughout its volume, and is placed with its cente at the oigin The sphee is suounded by an unchaged spheical conducting shell of inne adius, a, and oute adius, b (5) (a) Daw a diagam that includes this system and an appopiate Gaussian suface fo finding the electic field at a point inside the sphee a distance, < a, fom the cente a b (15) (b) Stat with Gauss law and find the electic field magnitude inside the insulato, ( < a) Show all the steps in you calculation, and expess you answe in tems of symbols given in the statement of the poblem, and numeical constants such as, k, o 0 E d A q enc 4 q enc V enc 3 π 3 V T 4 3 π a3 3 a 3 3 E (4π 2 a 3 ) E 4π a 3 (10) (c) Detemine the suface chage density, a, on the inne suface of the spheical conducting shell, and the suface chage density, b, on the oute suface of the spheical conducting shell E d A0 q enc a + b 0 In the conducto, E0 Thus 0+ a +σ a (4π a 2 ) +σ b (4π b 2 )0 4πa 2σ a σ b 4πb 2 (10) (d) Use Gauss law to find the electic field magnitude at points > b outside the conducting shell Expess you answe in tems of symbols given in the statement of the poblem, and numeical constants such as, k, o 0 E d A q enc E (4π 2 ) E 4π 2
9 A solid conducting sphee has a net positive chage,, and a adius, R (20) (a) Detemine the electic potential eveywhee due to the chaged sphee E d A q enc V E d Outside the sphee, E (4π 2 ) V d 4π 2 Since V ( )0, V () 4π E 4π 2 V 4π Inside the sphee, E0 Thus V 0 fo any two locations in the conducto, specifically, a location on the suface and any location inside Thus inside the sphee, V () 4π R (5) (b) Gaph the potential as a function of distance fom the cente of the sphee V R (15) (c) A poton is fied at the sphee fom a geat distance away with an initial speed, v o, and comes to a momentay stop at > R What will be the poton's minimum distance fom the cente of the sphee? [The position of the sphee is held fixed] U o +K o U f +K f 0+ 1 2 mv 2 o +0 4π f f 2mv 2 o π