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A particle B of charge Q and mass m floats in equilibrium under gravity and the electrostatic force from a fixed charge A located directly below it. If B is given a small vertical displacement, the equilibrium is:

1. stable
2. unstable
3. neutral
4. cannot be in equilibrium

Correct answer: unstable

Solution

At equilibrium the upward Coulomb force balances mg. If B moves up slightly, separation increases, the Coulomb force (proportional to 1/r²) decreases below mg, so net force is downward... but downward motion is toward A, decreasing r and increasing the Coulomb force above mg, pushing B further up. In each case the displacement is reinforced rather than opposed, so the vertical equilibrium is unstable.

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