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A solid metallic sphere of radius R having charge + 3Q is surrounded by a hollow spherical shell of radius 2 R and having a charge -Q. (a) Find electric field at distance r from centre of solid sphere [R lt rlt 2R]. (b) Find potential difference between sphere and shell. (c ) Find distribution of charge if (i) inner sphere is earthed (ii) inner sphere and shell are connected by a metallic wire. |
Answer» Solution : To find electeric field at `P`, assume charge inside sphere of radius `r` to be concentrated at centre `O`. `E_(P) = (1)/(4 pi in_(0)) .(3Q)/(r^(2))` (b) `V_(A) = (1)/(4 pi in_(0)) [ (3Q)/(R ) + (-Q)/(2R)]` `V_(B) = (1)/(4pi in_(0)) [ (3Q)/(2R) + (-Q)/(2R)]` `V_(A) - V_(B) = (1)/(4 pi in_(0)).(3Q)/(2R)` (c ) (i) LET charge on INNER sphere be `Q'`. `V_(P) = (1)/(4 pi in_(0)) [(Q')/(R ) + (-Q)/(2R)] = 0` `Q' = Q//2`  Charge distribution :  (II) When shell is connected to sphere , potential difference between shell and sphere becomes zero.  `V_(A) GT V_(B)` , charge `3Q` from sphere flows to shell , so that `V_(A) = V_(B)` Charge on sphere `= 0` Charge on shell `= 2q` |
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