PHYSICS · Multi-part · CBSE · Physics · Electric Charges and Fields · Electric Charges and Fields
Problem
A fixed point charge +Q rests at the origin. Directly above it on the y-axis, at a distance r0, a tiny ring-shaped bead of mass m carries a positive charge q and is observed to be momentarily at rest, levitating against gravity.
In answering the following, treat both objects as point charges, ignore any motion of Q, and neglect air resistance.
(a) Obtain an expression for q in terms of m, g, Q, r0, and fundamental constants that allows the bead to remain in static equilibrium at the distance r0.
(b) The bead is given a brief upward push so that its position is displaced to r=r0+Δr, where Δr≪r0, and released from rest. Derive an approximate expression for the bead’s initial vertical acceleration a(Δr), retaining only the leading non-zero term in Δr/r0.
(c) Based on your result in part (b), state whether the equilibrium at r=r0 is stable or unstable. Justify your answer with reference to the sign of the acceleration for small positive and negative displacements.