P2213_HW10_solns_Fall2008 - - 1 - Physics 2213 HW #10...

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Unformatted text preview: - 1 - Physics 2213 HW #10 Solutions Fall 2008 24.28 [Capacitor Energy] After the two capacitors are connected they must have equal potential difference, and their combined charge must add up to the original charge. / C Q V = . The stored energy is 2 2 1 2 2 Q U CV C = = (a) . Q CV = (b) 1 2 1 2 Q Q V C C = = and also 1 2 Q Q Q CV + = = . 1 C C = and 2 2 C C = so 1 2 ( 2) Q Q C C = and 1 2 2 Q Q = . 1 3 2 Q Q = . 1 2 3 Q Q = and 1 2 2 3 3 Q Q V V C C = = = . (c) 2 2 2 2 2 2 1 2 1 2 3 3 1 2 ( ) 2( ) 1 1 1 1 2 2 3 3 Q Q Q Q Q U CV C C C C C = + = + = = (d) The original U was 2 1 2 U CV = , so 2 1 6 U CV = - . (e) Thermal energy of capacitor, wires, etc., and electromagnetic radiation. The original charge of the charged capacitor must distribute between the two capacitors to make the potential the same across each capacitor. The voltage V for each after they are connected is less than the original voltage V of the charged capacitor. 23.32 [Metal Sphere Potential] Expressions for the electric potential inside and outside a solid conducting sphere are derived in Example 23.8. (a) This is outside the sphere, so 9 (3.50 10 C) 65.6 V. 0.480 m kq k V r- = = = (b) This is at the surface of the sphere, so 9 (3.50 10 C) 131V 0.240 m k V- = = . (c) This is inside the sphere. The potential has the same value as at the surface, 131 V. All points of a conductor are at the same potential. 23.35 [Potential of a Wire] The voltmeter measures the potential difference between the two points. We must relate this quantity to the linear charge density on the wire. For a very long (infinite) wire, the potential difference between two points is ( ) ln / 2 b a V r r = ....
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P2213_HW10_solns_Fall2008 - - 1 - Physics 2213 HW #10...

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