Three identical metallic uncharged spheres `A, B, and C,` each of radius `a`, are kept at the corners of an equilateral triangle of side `d(d gt gt a)` as shown in (Fig. 3.137). The fourth sphere (of radius a), which has a charge `q`, touches `A` and is then removed a position far away. `B` is earthed and then the earth connection is removed. `C` is then earthed. The charge on `C` is
.

Options

A. `(q a)/(2 d)((2 d - a)/(2 d))`
B. `(q a)/(2 d)((2 d - a)/( d))`
C. `-(q a)/(2 d)(( d - a)/( d))`
D. `-(2 q a)/( d)(( d - a)/(2 d))`

Answer

c

Explanation

`(k q_1)/a + (k q)/(2 d) = 0` or `q_1 = (-q a)/(2 d)`
`(k q_2)/a + (kq)/( 2d) + (k q_1)/d = 0` or `q_2 = (-q a)/(2 d)((d - a)/d)`
.