Two spherical conductors B and C having equal radii and cayying equal charges on them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that B but uncharged is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is

Options

A. `F//4`
B. `3F//4`
C. `F//8`
D. `3F//8`

Answer

4

Explanation

`F prop (q^(2))/(d^(2))`
When `A` is in contact with `B` , charge on `A` and `B` is `(q + 0)/(2) = (q)/(2)`
When `A` is in contact with `C` , charge on each `A` and `C` is
`(q + (q)/(2))/(2) = (3q)/(4)`
`F' prop ((q)/(2) .(3q)/(4))/(d^(2))`
`(F')/(F) = (3)/(8) rArr F' = (3F)/(8)`