Homework 1 Solutions

Homework 1 Solutions - lim (kl9356) Homework 1 Weathers...

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Unformatted text preview: lim (kl9356) Homework 1 Weathers (22202) 1 This print-out should have 8 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points 1) Two uncharged metal balls, X and Y , each stand on a glass rod and are touching. Y X 2) A third ball carrying a positive charge, is brought near the first two. Y X + 3) While the positions of these balls are fixed, ball X is connected to ground. Y X + 4) Then the ground wire is disconnected. Y X + 5) While X and Y remain in touch, the ball carring the positive charge is removed. Y X 6) Then ball X and Y are separated. Y X After these procedures, the signs of the charge q X on X and q Y on Y are 1. q X is negative and q Y is negative. cor- rect 2. q X is positive and q Y is positive. 3. q X is positive and q Y is neutral. 4. q X is negative and q Y is positive. 5. q X is negative and q Y is neutral. 6. q X is neutral and q Y is positive. 7. q X is positive and q Y is negative. 8. q X is neutral and q Y is negative. 9. q X is neutral and q Y is neutral. Explanation: When the ball with positive charge is brought nearby, the free charges inside X and Y rearrange themselves. The negative charges are attracted and go to the right ( i.e. move to Y ), whereas the positive charges are repelled and collect in the left hand side of the system X Y , i.e., in X . When we ground X , the positive charges which have collected in X are allowed to es- cape (they strive to the left), whereas the negative charges in Y are still held enthralled by the positive charge on the third ball. We break the ground. Now we remove the third ball with positive charge. The charge on Y is redistributed in the system X Y , i.e. they share the negative charge (equally if identical). Finally we separate X and Y . The signs of the charge on X and that on Y are both negative. 002 10.0 points Four point charges, each of magnitude 5 . 68 C, are placed at the corners of a square 92 . 8 cm on a side. The value of Coulombs constant is 8 . 98755 10 9 N m 2 / C 2 . lim (kl9356) Homework 1 Weathers (22202) 2 If three of the charges are positive and one is negative, find the magnitude of the force experienced by the negative charge. Correct answer: 0 . 644514 N. Explanation: Let : k e = 8 . 98755 10 9 N m 2 / C 2 , d = 92 . 8 cm = 0 . 928 m , and Q = 5 . 68 C = 5 . 68 10 6 C . F 24 F 34 F 14 + 3 + 1 + 2- 4 The forces are F 34 = F 24 = k e Q 2 d 2 = ( 8 . 98755 10 9 N m 2 / C 2 ) ( 5 . 68 10 6 C ) 2 (0 . 928 m) 2 = 0 . 336699 N F 14 = k e Q 2 ( 2 d ) 2 = 1 2 k e Q 2 d 2 = 1 2 F 34 The vector sum of F 24 and F 34 is in the same direction as F 14 , so F = F 14 + radicalBig F 34 2 + F 24 2 = 1 2 F 34 + radicalBig...
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Homework 1 Solutions - lim (kl9356) Homework 1 Weathers...

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