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For a point charge placed on the axis of a uniformly charged ring of radius a, at what axial distance x from the centre of the ring is the force on the charge maximum?

1. a/sqrt(3)
2. a/sqrt(2)
3. a/sqrt(6)
4. a/sqrt(5)

Correct answer: a/sqrt(2)

Solution

The axial force on a charge follows the ring's axial field, which rises from zero at the centre, peaks, then falls off. Differentiating and setting the derivative to zero yields x = a/sqrt(2).

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