problem22_65

University Physics with Modern Physics with Mastering Physics (11th Edition)

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22.65: a) The charge enclosed: . 5 8 24 15 24 11 4 ) 16 ( 3 ) 8 ( 8 ) / ( ) 2 ( 4 and , 6 3 ) 2 ( 4 where , 3 3 3 4 4 3 3 2 / 3 2 0 3 3 0 πR Q α απR Q απR R R R R R απ dr R r r α π Q απR R π Q Q Q Q R R i i = = = - - - = - = = = + = α b) . 15 8 3 3 4 4 : 2 3 0 0 0 3 2 R πε Qr ε αr E ε πr α πr E R r = = = = Φ enclosed. is charge all since , 4 : ). 1 ) ( 48 ) ( 64 ( 15 ) 1 ) ( 48 ) ( 64 ( ) 4 ( 24 4 ) 16 ( 3 ) 8 ( 8 1 4 : 2 2 0 4 3 2 4 3 2 0 3 4 4 3 3 0 0 2 r πε Q E R r R r R r r kQ R r R r πr ε απR E R R r R r απ ε ε Q πr E R r R i = - - = - - = - - - + = = Φ c) . 267 . 0 15 4 ) 15 / 4 ( = = = Q Q Q Q i d) , : 2 / 3 0 15 8 r eE F R r R πε eQ - = - = so the restoring force depends upon displacement to the first power, and we have simple harmonic motion.
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Unformatted text preview: e) . 8 15 2 2 , 15 8 , 15 8 , 3 3 3 eQ m R πε π ω π T m R πε eQ m k ω R πε eQ k kr F e e e = = = = =-= f) If the amplitude of oscillation is greater than , 2 / R the force is no longer linear in , r and is thus no longer simple harmonic....
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