PHY303L Solutions%204

PHY303L Solutions%204 - h o m ewo rk 04 – FAU S AK TAY L...

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Unformatted text preview: h o m ewo rk 04 – FAU S AK, TAY L OR – Du e: F e b 11 2008 , 4:00 am 1 Question 1, chap 26, sect 1. pa r t 1 of 1 10 p oi nts T wo l a r ge pa r a llel co ndu c t i n g p l at e s P and Q a r e co nn ec t e d t o a batt e r y of e m f E , as sh ow n. A t e st c ha r ge i s p l a ce d su cce ss i v el y at p oi nts I , II , and III . E + − I II III I f e d ge e ec ts a r e n egligi b le , th e fo r ce o n th e c ha r ge w h e n i t i s at p oi nt III i s 1. of e q ua l ma g n i tud e and i n th e sam e d i- r ec t io n as th e fo r ce o n th e c ha r ge w h e n i t i s at p oi nt I . 2. of e q ua l ma g n i tud e and i n th e sam e d i- r ec t io n as th e fo r ce o n th e c ha r ge w h e n i t i s at p oi nt II . correct 3. mu c h le ss i n ma g n i tud e than th e fo r ce o n th e c ha r ge w h e n i t i s at p oi nt II , but i n th e sam e d i r ec t io n. 4. e q ua l i n ma g n i tud e t o th e fo r ce o n th e c ha r ge w h e n i t i s at p oi nt I , but i n th e o pp o- s i t e d i r ec t io n. 5. mu c h g r e at e r i n ma g n i tud e than th e fo r ce o n th e c ha r ge w h e n i t i s at p oi nt II , but i n th e sam e d i r ec t io n. Explanation : N eglec t i n g e d ge e ec ts, th e elec t r ic fiel d st r e n g th b e t wee n th e t wo p l at e s i s un ifo r m. Th e r efo r e th e fo r ce o n th e t e st c ha r ge i s th e sam e at p oi nts II and III , b o th i n ma g n i tud e and i n d i r ec t io n. Wh e n e d ge e ec ts a r e n egligi b le , th e elec- t r ic fiel d st r e n g th at p oi nt I i s ze r o , s o th e fo r ce o n th e t e st c ha r ge i s ze r o w h e n i t i s at p oi nt I . Question 2, chap 26, sect 1. pa r t 1 of 1 10 p oi nts A sph e r ic a l c apa ci t o r co ns i sts of a co ndu c t- i n g ba ll of r ad i us 7 c m that i s ce nt e r e d i ns i d e a g r o und e d co ndu c t i n g sph e r ic a l sh ell of i nn e r r ad i us 10 c m. Th e C o u lo mb co nstant i s 8 . 98755 × 10 9 N m 2 / C 2 . What c ha r ge i s r e q u i r e d t o a c h ie v e a p o t e n- t i a l of 497 V o n th e ba ll of r ad i us 7 c m ? C o rr ec t ans we r : 1 . 2903 × 10 − 8 C (t ole r an ce ± 1 % ). Explanation : L e t : k e = 8 . 98755 × 10 9 N m 2 / C 2 , a = 7 c m = . 07 m , b = 10 c m = . 1 m , and V = 497 V . Th e c apa ci tan ce of a sph e r ic a l c apa ci t o r i s gi v e n by C = ab k e ( b − a ) . Th e c ha r ge r e q u i r e d t o a c h ie v e a p o t e nt i a l d i e r e n ce V b e t wee n th e sh ell and th e ba ll i s gi v e n by Q = C V = 1 k e abV ( b − a ) = 1 ( 8 . 98755 × 10 9 N m 2 / C 2 ) × ( . 07 m)( . 1 m)( 497 V) ( . 1 m) − ( . 07 m) = 1 . 2903 × 10 − 8 C . Question 3, chap 26, sect 1. pa r t 1 of 1 10 p oi nts A sma ll elec t r ic a ll y c ha r ge d o b j ec t i s sus- p e nd e d by a th r e ad b e t wee n th e v e r t ic a l p l at e s of a pa r a llel- p l at e c apa ci t o r ....
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PHY303L Solutions%204 - h o m ewo rk 04 – FAU S AK TAY L...

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