HW1-Solutions

# HW1-Solutions - Version PREVIEW HW1 feng (58230) 1 This...

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Unformatted text preview: Version PREVIEW HW1 feng (58230) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Three Point Charges 05 001 (part 1 of 2) 10.0 points Three charges are arranged as shown in the figure. The Coulomb cosnstant is 8 . 98755 10 9 N m 2 / C 2 . x y 3 . 1 nC 3 m . 6 nC . 72 nC 1 . 8 m Find the magnitude of the electrostatic force on the charge at the origin. Correct answer: 2 . 21044 nN. Explanation: Let : ( x , y ) = (0 m , 0 m) , q = . 6 nC , ( x 1 , y 1 ) = (3 m , 0 m) , q 1 = 3 . 1 nC , ( x 2 , y 2 ) = (0 m , 1 . 8 m) , and q 2 = 0 . 72 nC . x y q 1 x 1 q q 2 y 2 F The force vector F 10 (in the hatwider 10 direction, ) be- tween charge 6 10 10 C and 3 . 1 10 9 C is vector F 10 = + k e q q 1 x 2 1 ( ) = ( 8 . 98755 10 9 N m 2 / C 2 ) ( . 6 nC) (3 . 1 nC) (3 m) 2 = (1 . 85743 10 9 N) . The plus sign means the force vector F 10 is towards the positive x-axis. The force vector F 20 (in the hatwider 20 direction, + ) between charge 6 10 10 C and 7 . 2 10 10 C is vector F 20 = + k e q q 2 y 2 2 (+ ) = (8 . 98755 10 9 N m 2 / C 2 ) ( . 6 nC) (0 . 72 nC) ( 1 . 8 m) 2 = ( 1 . 19834 10 9 N) . The minus sign means the force vector F 20 is towards the negative y-axis. The magni- tude of the total force exerted on the charge 6 10 10 C is equal to bardbl vector F bardbl = radicalBig F 2 10 + F 2 20 = bracketleftBig (1 . 85743 10 9 N) 2 + ( 1 . 19834 10 9 N) 2 bracketrightBig 1 2 = 2 . 21044 10 9 N = 2 . 21044 N . 002 (part 2 of 2) 10.0 points What is the angle between the electrostatic force on the charge at the origin and the pos- itive x-axis? Answer in degrees as an angle between 180 and 180 measured from the positive x-axis, with counterclockwise posi- tive. Correct answer: 32 . 8285 . Explanation: The angle between vector F and the negative y- axis is = arctan parenleftbigg 1 . 19834 10 9 N 1 . 85743 10 9 N parenrightbigg = 32 . 8285 . Version PREVIEW HW1 feng (58230) 2 keywords: Two Metal Spheres 003 (part 1 of 2) 10.0 points Two identical small metal spheres with q 1 &gt; and | q 1 | &gt; | q 2 | attract each other with a force of magnitude 92 . 4 mN, as shown in the figure below. F 21 F 12 bardbl vector F bardbl = 92 . 4 mN 3 . 93 m q 1 q 2 r 1 = 24 m r 2 = 24 m Figure 1: Before touching The spheres are then brought together until they are touching. At this point, the spheres are in electrical contact so that the charges can move from one sphere to the other until both spheres have the same final charge, q ....
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## This note was uploaded on 04/27/2010 for the course PHY 303L taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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HW1-Solutions - Version PREVIEW HW1 feng (58230) 1 This...

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