A spherical metal shell A of radius `R_A` and a solid metal sphere B of radius `R_B(ltR_A)` are kept far apart and each is given charge `'+Q'`. Now they are connected by a thin metal wire. Then

Options

A. `(i),(ii)`
B. `(i),(ii),(iii)`
C. `(i),(ii),(iv)`
D. All

Answer

4

Explanation

`Q_(A) + Q_(B) = 2Q` ….(i)
`(1)/(4 pi in_(0)) .(Q_(A))(R_(A)) = (1)/(4 pi in_(0)) .(Q_(B))/(R_(B))` …..(ii)
From (i) and (ii) ,
`Q_(A) = A_(B)((R_(A))/(R_(B)))`
`Q_(B) ((R_(A))/(R_(B)) + 1) = 2Q`
`Q_(B) = (2Q R_(B))/(R_(A) + R_(B)) , Q_(A) = (2 QR_(A))/(R_(A) + R_(B))`
Since `R_(A) gt R_(B)` i.e. `Q_(A) gt Q_(B)`
`(sigma_(A))/(sigma_(B)) = (Q_(A)//4 pi R_(A)^(2))/(Q_(B)//4 pi R_(B)^(2)) = (R_(A))/(R_(B)) . ((R_(B))/(R_(A)))^(2) = (R_(B))/(R_(A)) , sigma_(A) lt sigma_(B)`
`E_(A) = (sigma_(A))/(in_(0)) , E_(B) = (sigma_(B))/(in_(0)) rArr E_(A) lt E_(B)`