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Unformatted text preview: Platt, David Oldquiz 2 Due: Oct 16 2005, 4:00 am Inst: Ken Shih 1 This print-out should have 27 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 3) 10 points Consider a long coaxial arrangement with a cylindrical wire of radius a along the axis of a thin cylindrical shell of radius b . There is a charge of- Q on the inner wire and charge of + Q on the outer shell. The figure below shows a short segment (length ) of the coaxial cable. Assume the length is much greater than the radii of the cylinders ( b ). + Q , b P , r- Q , a The magnitude of the electric field at P where P is at a radius r , between the wire and the shell, is given by 1. k ~ E k = Q 2 r 2 . 2. k ~ E k = Q 2 4 r 2 . 3. k ~ E k = Q 2 r . 4. k ~ E k = Q 2 r . correct 5. None of these 6. k ~ E k = Q 4 r 2 . 7. k ~ E k = Q 2 2 r . 8. k ~ E k = Q 2 2 r . 9. k ~ E k = Q 2 4 r 2 . Explanation: Construct a Gaussian cylinder at radius r (for a < r < b ). The charge enclosed is the charge on the wire, + Q . Thus, = I ~ E d ~ A = Q E 2 r = Q r k ~ E k = Q 2 r . In the second step the following reasoning was used. The total flux coming out from the cylindrical Gaussian surface is the sum of ends , the flux coming out from the ends of the cylinder and side the flux coming out from the side of the cylinder. For large compared with a and b we can neglect ends and take the electric field to be radial, so = side = E 2 r . Since ~ E points radially, ~ E = Q 2 r r . 002 (part 2 of 3) 10 points The magnitude of the potential difference be- tween the two conductors is given by 1. | V | = Q 4 1 a- 1 b . 2. | V | = Q 2 2 ln b a . 3. | V | = Q 2 2 ln b a . 4. | V | = Q 4 1 a- 1 b . Platt, David Oldquiz 2 Due: Oct 16 2005, 4:00 am Inst: Ken Shih 2 5. | V | = Q 2 ln b a . correct 6. None of these 7. | V | = Q 2 ln b a . 8. | V | = Q 2 4 1 a- 1 b . 9. | V | = Q 2 4 1 a- 1 b . Explanation: The absolute value of the potential differ- ence is given by the expression V =- Z ~ E d ~ . This is a line integral along a radius vector from r = a to r = b . Thus, d ~ = dr r. | V | = Z b a Q 2 r dr r r . Since r is a unit vector, r r = 1 . Thus, | V | = Q 2 Z b a dr r = Q 2 ln b a . 003 (part 3 of 3) 10 points Given: The capacitance C , the length , and radius of the cylindrical shell b as shown in the figure....
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