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13_Ch 16 College Physics ProblemCH16 Electrical Energy and Capacitance

13_Ch 16 College Physics ProblemCH16 Electrical Energy and Capacitance

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Electrical Energy and Capacitance 47 16.18 Outside the spherical charge distribution, the potential is the same as for a point charge at the center of the sphere, e V k Q r = ( ) , where Thus, 9 1.00 10 C Q = × ( ) 1 1 e e f i ek Q r r = − PE q V = and from conservation of energy ( ) ( ) e PE −∆ KE = , or 2 1 1 0 2 e e f i m v ek Q r r = − − 1 This gives 2 1 1 e e f i k Qe m r r = v , or ( )( ) 2 19 2 N m 2 8.99 10 10 C C 1 1 9. 0.020 0 m 0.030 0 m v × = 9 9 31 1.00 10 C 1.60 11 10 kg × × × 6 7.25 10 m s v = × 16.19 From conservation of energy, ( ) ( ) e e f i KE PE KE PE + = + , which gives 2 1 0 0 2 e i f k Qq m v r α + = + or ( )( ) 2 2 2 79 2 2 e e f i i k e e k Qq r m v m v α α = = ( ) ( ) ( ) ( ) 2 2 9 19 2 14 2 27 7 N m 2 8.99 10 158 1.60 10 C C 2.74 10 m 6.64 10 kg 2.00 10 m s f r × × = = × × × 16.20 By definition, the work required to move a charge from one point to any other point on an equipotential surface is zero. From the definition of work,
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