Homework_02

# Homework_02 - Nguyen, Thanh Homework 2 Due: Jan 25 2008,...

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Unformatted text preview: Nguyen, Thanh Homework 2 Due: Jan 25 2008, 7:00 pm Inst: Weathers 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Four point charges are placed at the four cor- ners of a square, where each side has a length a . The upper two charges have identical pos- itive charge, and the two lower charges have charges of the same magnitude as the first two but opposite sign. That is, q 1 = q 2 = q and q 3 = q 4 =- q where q > 0. q 4 q 2 q 3 q 1 P j i Determine the direction of the electric field at the center, point P. 1.- j correct 2.- 1 2 ( i- j ) 3.- 1 2 ( i + j ) 4. j 5.- i 6. i 7. 8. 1 2 ( i + j ) 9. 1 2 ( i- j ) Explanation: The direction is already clear: all the x- components cancel, and the lower charges at- tract and the top ones repel, so the answer is- j . keywords: 002 (part 1 of 2) 10 points Three positive charges are arranged as shown at the corners of a rectangle. The Coulomb constant is 8 . 98755 10 9 N m 2 / C 2 . + + + . 417 m 1 . 251 m 2 . 28 nC 1 . 14 nC 7 . 56 nC Find the magnitude of the electric field at the fourth corner of the rectangle. Correct answer: 87 . 1599 N / C. Explanation: r 1 r 2 Q 2 Q 1 Q 3 E 1 E 2 E 3 Let : q 1 = 1 . 14 nC = 1 . 14 10- 9 C , q 2 = 2 . 28 nC = 2 . 28 10- 9 C , q 3 = 7 . 56 nC = 7 . 56 10- 9 C , r 2 = 1 . 251 m , r 1 = 0 . 417 m , and k e = 8 . 98755 10 9 N m 2 / C 2 . The length of the diagonal is r 3 = q r 2 1 + r 2 2 = q (1 . 251 m) 2 + (0 . 417 m) 2 = 1 . 31867 m . The electric field produced by the charge q 1 is along the positive y-axis, so E 1 ,x = 0 E 1 ,y = E 1 = k c q 1 r 2 1 . Nguyen, Thanh Homework 2 Due: Jan 25 2008, 7:00 pm Inst: Weathers 2 The electric field produced by the charge q 2 is along the negative x-axis, so E 2 ,x =- E 2 =- k c q 2 r 2 2 E 2 ,y = 0 . The electric field produced by the charge q 3 is upward and to the left along the diagonal of the rectangle, and is directed away from the charge since q 3 is positive, so E 3 = k e q 3 r 2 3 . Consider the direction of E 3 cos = r 2 r 3 and sin = r 1 r 3 Thus E 3 ,x =- k e q 3 r 2 3 sin =- k e q 3 r 2 r 3 3 E 3 ,y = k C q 3 r 2 3 cos = k e q 3 r 1 r 3 3 , so that E net,x = E 2 ,x + E 3 ,x =- k e q 2 r 2 2- k e q 3 r 2 r 3 3 =- ( 8 . 98755 10 9 N m 2 / C 2 ) 2 . 28 10- 9 C (1 . 251 m) 2- ( 8 . 98755 10 9 N m 2 / C 2 ) (7 . 56 10- 9 C) (1 . 251 m) (1 . 31867 m) 3 =- 50 . 1628 N / C , and E net,y = E 1 ,y + E 3 ,y = k e q 1 r 2 1 + k e q 3 r 1 r 3 3 = ( 8 . 98755 10 9 N m 2 / C 2 ) 1 . 14 10- 9 C (0 . 417 m) 2 + ( 8 . 98755 10 9 N m 2 / C 2 ) (7 . 56 10- 9 C) (0 . 417 m) (1 . 31867 m) 3 = 71 . 2779 N / C , so that E net = q E net,x 2 + E net, 4 2 E net = (- 50 . 1628 N / C) 2 +(71 . 2779 N / C) 2 / 1 2 = 87 . 1599 N / C ....
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## This note was uploaded on 10/24/2011 for the course PHYS 2220 taught by Professor Littler during the Spring '00 term at North Texas.

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Homework_02 - Nguyen, Thanh Homework 2 Due: Jan 25 2008,...

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