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Unformatted text preview: saldana (avs387) homework 10 Turner (56705) 1 This printout should have 12 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 2) 10.0 points A long coaxial cable consists of an inner cylin drical conductor with radius R 1 and an outer cylindrical conductor shell with inner radius R 2 and outer radius R 3 as shown. The ca ble extends out perpendicular to the plane shown. The charge on the inner conductor per unit length along the cable is and the corresponding charge on the outer conductor per unit length is (same in magnitudes but with opposite signs) and > 0. Q R 1 R 2 R 3 b Q Find the magnitude of the electric field at the point a distance r 1 from the axis of the inner conductor, where R 1 < r 1 < R 2 . 1. E = R 1 3 r 1 2 2. E = 2 r 1 correct 3. E = 3 r 1 4. None of these. 5. E = R 1 4 r 1 2 6. E = 0 7. E = 2 R 1 4 r 1 2 8. E = 2 R 1 9. E = 2 3 r 1 10. E = 2 r 1 Explanation: Pick a cylindrical Gaussian surface with the radius r 1 and apply the Gausss law; we obtain E 2 r 1 = Q E = 2 r 1 002 (part 2 of 2) 10.0 points For a 100 m length of coaxial cable with inner radius 0 . 521642 mm and outer radius 1 . 55345 mm. Find the capacitance C of the cable. Correct answer: 5 . 09804 nF. Explanation: Let : = 100 m , R 1 = 0 . 521642 mm , and R 2 = 1 . 55345 mm . We calculate the potential across the capaci tor by integratingE d s. We may choose a path of integration along a radius; i.e.,E d s =E dr . V = 1 2 q l integraldisplay R 1 R 2 dr r = 1 2 q l ln r vextendsingle vextendsingle vextendsingle vextendsingle R 1 R 2 = q 2 l ln R 2 R 1 . Since C = q V , we obtain the capacitance C = 2 l ln parenleftbigg R 2 R 1 parenrightbigg = 2 (8 . 85419 10 12 c 2 / N m 2 ) ln parenleftbigg 1 . 55345 mm . 521642 mm parenrightbigg (100 m) = 5 . 09804 nF . saldana (avs387) homework 10 Turner (56705) 2 003 10.0 points Given a spherical capacitor with radius of the inner conducting sphere a and the outer shell b . The outer shell is grounded. The charges are + Q and Q . A point C is located at r = R 2 , where R = a + b . a A B C + Q Q b What is the capacitance of this spherical capacitor?...
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This note was uploaded on 10/26/2010 for the course PHYS 56705 taught by Professor Turner during the Spring '10 term at University of Texas at Austin.
 Spring '10
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