Two equally charged identical metal spheres A and B repel each other with a force `2 xx 10^(-5) N` . Another identical unchanged sphere C is touched to B and then placed at the mid-point between A and B . What is the net electric force on C ?

Explanation

Let q be charge on each sphere A and B separated by a distance r , then force between them is
`F_(1) = (kq^(2))/(r^(2)) = 2 xx 10^(5) ` N (given)

When C touches B then charges on C and B will be `q/2` on each sphere . When C is placed at mid-point of A and B then ,

Force between B and C is
`F_(2) = (k (q/2)^(2))/((r/2)^(2)) = (kq^2)/(r^2)`
Force between A and C is
`F_(3) = (k (q/2) q)/((r/2)^(2)) = 2 ((kq^2)/(r^2))`
Resultant of force `F_(3)` and `F_(2)` is `|F| = |F_(3)| - |F_(2)|`
`= 2((kq^2)/(r^2)) - ((kq^2)/(r^2))`
`= (kq^2)/(r^2) = 2 xx 10^(-5) N`
and its direction is towards A .