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. `E_(A_(inside)) = 0`
B. `Q_(A) gt Q_(B)`
C. `(sigma_(A))/(sigma_(B)) = (R_(B))/(R_(A))`
D. `E_(A)` on the surface `lt E_(B)` on surface

Answer

A, B, C, D

Explanation

In a conductor, electric field is zero. Therefore, `E_(A)` inside = Zero
After connection, `V_(A) = V_(B) implies (KQ_(A))/(R_(A)) = (K Q_(B))/(R_(B))`
`(Q_(A))/(Q_(B)) = (R_(A))/(R_(B))` As `R_(A) gt R_(B) :. Q_(A) gt Q_(B)`
`sigma_(A) = (Q_(A))/(4pi in_(0) R_(A) 2) , sigma_(B) = (Q_(B))/(4pi in_(0) R_(B) 2)`
`implies (sigma_(A))/(sigma_(B)) = (R_(B))/(R_(A))`
`(E_(A)" on surface")/(E_(B)" on surface") = (sigma_(A)//in_(0))/(sigma_(B)//in_(0)) = (sigma_(A))/(sigma_(B)) = (R_(B))/(R_(A))`
As `R_(B) lt R_(A)`
`:. E_(A)` on surface `lt E_(B)` on surface