Two small beads having positive charges 3q and q are fixed at the opposite ends of a horizontal, insulating rod, extending from the origin to the point x=d as shown in fig. A third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium? Can it be in stable equilibrium ?

Answer

`(sqrt(3)d)/(sqrt(3)+1)`

Explanation

For Q to be in equilibrium
`(k3qQ)/(x^(2)) =(kQq)/((d-x)^(2))`
or , `x=(sqrt(3)d)/(sqrt(3)+1)`
The bead can be in stable equilibrium, if it has positive charges.