HW-7Solutions-01-26-08

HW-7Solutions-01-26- - Physics 21 Spring 2008 HW-7 Solutions 7-1(HRW 25-53 The space between two concentric conducting spherical shells of radii b

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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 00 4. ab C ba 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 92 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 κε == = −× π (b) The charge on the positive plate is (0.107 nF)(73.0 V) 7.79 nC. qC V = (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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This note was uploaded on 02/20/2008 for the course PHYSIC 2 taught by Professor Kim during the Spring '08 term at Lehigh University .

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HW-7Solutions-01-26- - Physics 21 Spring 2008 HW-7 Solutions 7-1(HRW 25-53 The space between two concentric conducting spherical shells of radii b

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