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A c h a r ge - 2 q i s p l ace d on t he i nn e r s ph e r i ca l t h i n c ondu c ti ng s h e ll , a nd a c h a r ge of + q i s p l ace d on t he ou t e r s ph e r i ca l t h i n c ondu c ti ng s h e ll . T he r a d i us of t he i nn e r s h e l l i s a a nd t he r a d i us of t he ou t e r s h e l l i s b . ( a ) De t e r mi ne t he e l ec t r i c f i e l d ( m a gn it ude a nd d i r ec ti on) i n t he f o ll o w i ng r e g i ons ( s how yo u r w o r k ) : R e g i on I : r ≤ a R e g i on II : a ≤ r ≤ b R e g i on III : r ≥ b ( b) F i nd t he a m ou n t of c h a r ge r e s i d i ng on t he i n s i d e s u rf ac e of eac h c ondu c ti ng s h e ll . J u s ti f y your a n s we r s ! ( c ) Fi nd t he a m ount of c h a r ge r e s i d i ng on t he o u t s i d e s u rf ac e of eac h c ondu c ti ng s h e ll . J u s ti f y your a n s we r s . ( d) O n t he f i g u r e on t he p r e v i ous p a g e , s k e t c h t he e l ec t r i c f i e l d l i n e s a ss o c i a t e d w it h t h e s e c h a r g e d s h e ll s . ( e ) S k e t c h qu a l i t a ti v e l y a g r a ph of E v e r s us r on t h e a x e s b e l o w .


 

 
 
A charge -2q is placed on the inner spherical thin conducting shell, and a charge of +q is placed on the outer spherical thin conducting shell.  The radius of the inner shell is a and the radius of the outer shell is b.

 

(a) Determine the electric field (magnitude and direction) in the following regions (show your work):

 

Region I: r ≤ a

 

Region II: a ≤ r ≤ b

 

 Region III: r ≥ b


(b) Find the amount of charge residing on the inside surface of each conducting shell.  Justify your answers!

 (c) Find the amount of charge residing on the outside surface of each conducting shell. Justify your answers.

  

(d) On the figure on the previous page, sketch the electric field lines associated with these charged shells.

 

(e) Sketch qualitatively a graph of E versus r on the axes below.

 


Grade:11

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