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A thin spherical conducting shell of radius r_(1) carries a charge Q. Concentric with it is another thin metallic spherical shell of radius r_(2) (r_(2) gt r_(1)). Calculate electric field at distance r when (i) r lt r_(1) ,(ii) r_(1) lt r lt r_(2) and (iii) r gt r_(2). What will be the field in above cases if outer shell (a) is given charge q and (b) is earthed ? |
Answer» Solution :We KNOW that electric field inside a conductor is zero and for EXTERNAL point , whole CHARGE is assumed to be concentrated at centre. (i) `r lt r_(1) , E = 0` (ii) `r_(1) lt r lt r_(2) , E = (1)/(4pi in_(0)) (Q)/(r^(2))` (iii) `r gt r_(2) , E = (1)/(4 pi in_(0)) (Q)/(r^(2))` (a)  (i) `r lt r_(1) , E = 0` (ii) `r_(1) lt r lt r_(2) , E = (1)/(4 pi in_(0)) (Q)/(r^(2))` (iii) `r gt r_(2) , E = (1)/(4 pi in_(0)) ((Q + q))/(r^(2))` (b)  (i) `r lt r_(1) , E_(0)` (ii) `r_(1) lt r lt r_(2) , E = (1)/(4 pi in_(0)) (Q)/(r^(2))` (iii) Due to eathing , charge on inner surface on outer shell is `-Q`. Therefore, `r gt r_(2) , E = 0` |
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