13_Chapter 16 HomeworkCH16 Electrical Energy and Capacitance

13_Chapter 16 HomeworkCH16 Electrical Energy and...

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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 VkQ r = () , where Thus, 9 1.00 10 C Q 11 ee f i ek Q rr  =   PE q V ∆= and from conservation of energy ( ) ( ) e PE KE , or 2 0 2 fi mv ekQ   −= −−  1 This gives 2 e ef i kQe mrr =− v , or ( ) 2 1 9 2 Nm 2 8.99 10 10 C C 9. 0.020 0 m 0.030 0 m v × 99 31 1.00 10 C 1.60 11 10 kg ×× × 6 7.25 10 m s v 16.19 From conservation of energy, ( ) ( ) f i KE PE KE PE += + , which gives 2 1 00 2 e i f kQq r α + or ( )( ) 22 27 92 2 e e f ii ke e r αα == 2 2 91 9 2 14 2 27 7 28 . 9 9 1 0 1 5 8 1 . 6 0 1 0 C C 2.74 10 m 6.64 10 kg 2.00 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, ( ) cos WF s θ = , the work is zero only if or 0 s = cos 0 F = . The displacement s cannot be assumed to be zero in all cases. Thus, one must require that
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