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The potential energy of a particle in a force field is U = A / r² - B / r, where A and B are positive constants and r is the distance of the particle from the centre of the field. For stable equilibrium, the distance of the particle is:

1. A / 2B
2. 24 / B
3. A / B
4. B / 4

Correct answer: A / 2B

Solution

For stable equilibrium, the force acting on the particle must be zero, which is derived from the condition dU/dr = 0. Differentiating U = A/r² - B/r with respect to r and solving for r gives r = A / 2B.

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