A small, electrically charged bead can slide on a circular, frictionless, thin, insulating ring. Charge on the bead is Q and its mass is m . A small electric dipole, having dipole moment P is fixed at the centre of the circle with the dipole’s axis lying in the plane of the circle. Initially, the bead is held on the perpendicular bisector of the dipole (see fig.) Ignore gravity and answer the following questions.
(a) Write the speed of the bead when it reaches the position `theta` shown in the figure. (b) Find the normal force exerted by the ring on the bead at position `theta`. (c) How does the bead move after it is released? Where will the bead first stop after being released? (d) How would the bead move in the absence of the ring?

Answer

(a). `v=sqrt(2-(QKPcostheta)/(mr^(2)))`
(b). Zero
(c). The bead oscillates. It stops at a point dametrically opposite to its starting point.
(d). Exactly same as it would move in the presence of the ring