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Unformatted text preview: mcconnell (kam2342) oldhomework 02 Turner (60230) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 4) 10.0 points A uniformly charged circular arc AB of radius R is shown in the figure. It covers a quarter of a circle and it is located in the second quadrant. The total charge on the arc is Q > 0. x y + + + + + + + + + R x y I II III IV B A O s R The direction of the electric field E due to the charge distribution at the origin is 1. along the negative y-axis. 2. in quadrant II. 3. in quadrant III. 4. in quadrant I. 5. along the positive y-axis. 6. along the positive x-axis. 7. along the negative x-axis. 8. in quadrant IV. correct Explanation: The electric field for a positive charge is directed away from it. In this case, the electric field generated by each q is going to be in quadrant IV, so the total electric field will be in the same quadrant. 002 (part 2 of 4) 10.0 points Determine E x , the x-component of the elec- tric field vector at the origin O due to the charge element q located at an angle sub- tended by an angular interval . 1. E x = k Q R 2 2 sin 2. E x = k Q R 2 cos 3. E x = k Q 2 R cos 4. E x = k Q 2 R 2 2 cos 5. E x = k Q R 2 sin 6. E x = 0 7. E x = k Q R sin 8. E x = k Q 2 R 2 cos 9. E x = k Q R 2 2 cos correct 10. E x = k Q R 2 2 cos Explanation: E = k q R 2 . The charge q per unit arc-length s is Q 2 R = 2 Q R , so q = s = R = 2 Q R R = 2 Q . On the other hand, the vector vector E makes an angle with the x-axis, so E x = k Q R 2 2 cos . 003 (part 3 of 4) 10.0 points Find E x , the electric field at the origin due mcconnell (kam2342) oldhomework 02 Turner (60230) 2 to the full arc length for the case where Q = 3 . 6 C and R = 0 . 69 m . Correct answer: 43263 . 9 N / C. Explanation: Let : Q = 3 . 6 C and R = 0 . 69 m . E x can be found by integrating the contribu- tions of all the q s in the arc. We get E x = integraldisplay / 2 k Q R 2 2 cos d = 2 k Q R 2 = 2 k (3 . 6 C) (0 . 69 m) 2 = 43263 . 9 N / C ....
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