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 particle from the centre of the field. For stable equilibrium the distance of the particle is

Question

Dr. Abubacker · Accepted Answer

[Solution from source] Equilibrium needs dU/dr = −2A/r³ + B/r² = 0, giving r = 2A/B. At this r, d²U/dr² = 6A/r⁴ − 2B/r³ = B⁴/(8A³) > 0, so U is a minimum and the equilibrium is stable. A/B is where U itself is zero, not where the force is zero. Answer (3).

Q. 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 particle from the centre of the field. For stable equilibrium the distance of the particle is

Explanation

Reviewed by Dr. Abubacker

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