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Unformatted text preview: benavides (jjb2356) homework 11 Turner (59130) 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 &gt; 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 &lt; r 1 &lt; R 2 . 1. E = R 1 4 r 1 2 2. E = 2 r 1 3. None of these. 4. E = 3 r 1 5. E = 2 R 1 4 r 1 2 6. E = 2 3 r 1 7. E = 2 r 1 correct 8. E = 0 9. E = 2 R 1 10. E = R 1 3 r 1 2 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 . 498411 mm and outer radius 1 . 54607 mm. Find the capacitance C of the cable. Correct answer: 4 . 91433 nF. Explanation: Let : = 100 m , R 1 = 0 . 498411 mm , and R 2 = 1 . 54607 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 . 54607 mm . 498411 mm parenrightbigg (100 m) = 4 . 91433 nF . benavides (jjb2356) homework 11 Turner (59130) 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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 Spring '08
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