problem23_88

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

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23.88: a) r V E a r a r ε a ρ V a r - = + - = and 2 3 1 18 : 3 3 2 2 0 2 0 . 3 6 6 18 2 2 0 0 3 2 2 0 2 0 - = + - - = a r a r ε a ρ a r a r ε a ρ E . 0 and 0 : = - = = r V E V a r b) 2 2 2 0 0 0 2 4 3 4 : πr a r a r ε a ρ ε Q πr E a r r r - = = . 3 4 1 4 3 3 ) ( 1 2 2 2 3 4 4 ) ( ) 2 ( 4 ) 2 ( 3 ) 2 ( 4 0 0 2 2 0 2 0 0 2 0 2 2 2 0 0 0 2 - = - = + - + - = - + + - + = = + + + + a r ρ a r ρ r ρ a a r a a r ε dr πr a ρ ε dr πr r ρ ε Q Q dr r r π a dr r r a dr r ε a ρ ε Q rdr r π E r dr r dr r dr r c) , 0 ) ( : = r ρ a r so the total charge enclosed will be given by: =
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