HW-7Solutions-01-26-08

# HW-7Solutions-01-26-08 - Physics 21 Spring 2008 HW-7...

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Physics 21, Spring 2008 January 26, 2008 HW-7 Solutions 7-1. (HRW 25-53) The space between two concentric conducting spherical shells of radii b = 1.70 cm and a = 1.20 cm is filled with a substance of dielectric constant κ = 23.5. A potential difference V = 73.0 V is applied across the inner and outer shells. Determine (a) the capacitance of the device, (b) the free charge q on the inner shell, and (c) the charge q’ induced along the surface of the inner shell. Solution: (a) According to Eq. 25-17 the capacitance of an air-filled spherical capacitor is given by 0 0 4 . ab C b a ε = π When the dielectric is inserted between the plates the capacitance is greater by a factor of the dielectric constant κ . Consequently, the new capacitance is 0 9 2 2 23.5 (0.0120 m)(0.0170 m) 4 0.107 nF. 8.99 10 N m C 0.0170 m 0.0120 m ab C b a κε = = = × π (b) The charge on the positive plate is (0.107 nF)(73.0 V) 7.79 nC. q CV = = = (c) Let the charge on the inner conductor be – q . Immediately adjacent to it is the induced charge q' . Since the electric field is less by a factor 1/

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• Spring '08
• Kim
• Physics, Energy, Potential difference, Electric charge, Dielectric

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