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A spherical metal shell A of radius RA a...

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

A

`E_(A)^("inside")` = 0

B

`Q_(A) gt Q_(B)`

C

`sigma_A/sigma_B = R_B/R_A`

D

`E_(A)^("on surface") lt E_(B)^("on surface")`

Text Solution

Verified by Experts

From Eqs. (I) and (ii)
`(Q_(A))/(Q_(B)) = (R_(A))/(R_(B))`
Solving Eqs. (i) and (ii) we get
`Q_(A) = (2QR_(A))/(R_(A) + R_(B))` and `Q_(B) = (2QR_(B))/(R_(A) + R_(B))` or `Q_(A) gt Q_(B)`
`(sigma_(A))/(sigma_(B)) = (Q_(A) // 4 piR_(A)^(2))/(Q_(B) // 4 pi R_(B)^(2)) = (R_(B))/(R_(A))` using Eq. (iii) ,
`Q_(B) gt Q_(A)` (as `R_(A) gt R_(B)`)
On surface, `E_(A) = (sigma_(A))/(epsilon_(0))` and `E_(B) = (sigma_(B))/(epsilon_(0))`
or `E_(A) lt E_(B)` `( :' sigma_(A) lt sigma_(B))`
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