A uniform non-conducting ring carries two fixed positive charges q and q′ on its circumference 90° apart. In a uniform upward electric field, the ring is in rotational equilibrium at an angle satisfying tanθ = q′/q. The nature of this rotational equilibrium is:
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Question

A uniform non-conducting ring carries two fixed positive charges q and q′ on its circumference 90° apart. In a uniform upward electric field, the ring is in rotational equilibrium at an angle satisfying tanθ = q′/q. The nature of this rotational equilibrium is:

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G1 Physics · Accepted Answer

The electric torque can be written as τ(θ) = ER[q′cosθ - qsinθ]. At equilibrium, q′cosθ = qsinθ. Now, dτ/dθ = ER[-q′sinθ - qcosθ] < 0. Therefore a small angular displacement produces a restoring torque. The equilibrium is stable.