A solid metallic sphere of radius a is surrounded by a conducting spherical shell of radius `b(bgt a)`. The solid sphere is given a charge Q. A student measures the potential at the surface of the solid sphere as V and the potential at the surface of spherical shell as `V_b`. After taking these readings, he decides . to put charge of `-4Q` on the shell. He then noted the readings of the potential of solid sphere and the shell and found that the potential difference is `/_\V` .
He then connected the outer spherical shell to the earth by a conducting wire and found that the charge on the outer surface of the shell as He then decides to remove the earthing connection from the shell and earthed the inner solid sphere. Connecting the inner sphere with the earth he observes the charge on the solid sphere as `q_2`. He then wanted to check what happens if the two are connected by the conducting wire. So he removed the earthing connection and connected a conducting wire between the solid sphere and the spherical shelll. After the connections were made he found the charge on the outer shell as `q_3`.
`q_3` is

Options

A. `(Q(a+b))/(a-b)`
B. `(Qa^2)/b`
C. `(Q(a-b))/b`
D. `-(Qb)/a`

Answer

C

Explanation

Whole inner charge transfers to shell.
`:.` Total charge on shell `=q_2-Q`
`=Q(a/b-1)`