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Unformatted text preview: homework 15 KIM, JI Due: Feb 18 2008, 4:00 am 1 Question 1, chap 23, sect 1. part 1 of 1 10 points Four point charges are placed at the four corners of a square. Each side of the square has a length L . b b b b b q 1 = q q 3 = q q 2 = q q 4 = q P L L Find the magnitude of the electric field vec- tor vector E at the center P of the square. 1. 2 2 k q L 2 2. 4 k q 2 L 3. k q 2 L 2 4. k q L 5. 2 2 k q L 6. k q L 2 7. 2 2 k q 2 L 2 8. 4 k q 2 L 2 9. 4 k q L 2 correct Explanation: The electric field is vector E = summationdisplay i vector E i = summationdisplay i k q i r 2 i r i . Each charge is at a distance L 2 from P, so the magnitude of each field is E = k q parenleftbigg L 2 parenrightbigg 2 = 2 k q L 2 . Consider the direction of each field: E 2 E 4 E 1 E 3 E 2 and E 4 cancel, so bardbl vector E bardbl = bardbl vector E 1 bardbl + bardbl vector E 3 bardbl = 2 | E 1 | = 4 k q L 2 . Question 2, chap 22, sect 5. part 1 of 1 10 points Two uncharged metal balls X and Z stand on insulating glass rods. A third ball, carrying a negative charge, is brought near the ball Z as shown in the figure. A conducting wire is then run between X and Z and then removed. Finally the third ball is removed. Z X conducting wire When all this is finished 1. ball X is negative and ball Z is neutral. 2. ball X is positive and ball Z is negative. 3. balls X and Z are both positive, but ball X carries more charge than ball Z . 4. ball X is positive and ball Z is neutral. 5. ball X is negative and ball Z is positive. correct homework 15 KIM, JI Due: Feb 18 2008, 4:00 am 2 6. balls X and Z are still uncharged. 7. balls X and Z are both positive, but ball Z carries more charge than ball X . 8. ball X is neutral and ball Z is positive. 9. ball X is neutral and ball Z is negative. 10. balls X and Z are both negative. Explanation: When the conducting wire is run between X and Z , some negative charge flows from Z to X under the influence of the negative charge of the third ball. Therefore, after the wire is removed, X is negatively charged and Z is positively charged. Question 3, chap 23, sect 3. part 1 of 1 10 points Consider symmetrically placed rectangular insulators with uniformly charged distribu- tions of equal magnitude as shown in the fig- ure below. x y + + + + How is the net field aligned at the origin? 1. aligned with the negative x-axis correct 2. along the 60 degree direction 3. along the 45 degree direction 4. aligned with the positive x-axis 5. along the 315 degree direction 6. aligned with the negative y-axis 7. along the 225 degree direction 8. along the 135 degree direction 9. along the 30 degree direction 10. aligned with the positive y-axis Explanation: At the origin, the positive slab of charge produces an electric field pointed toward quadrant III (away from the positively charged slab). The negatively charged slab produces an electric field of equal magnitude (as the positively charged slab) but pointing...
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