The potential energy of a force field is: U = $\frac{A}{r^{2}} - \frac{B}{r}$ B are positive constants and r is the distance of particle from the field. For stable equilibrium, the distance of the particle is :

A/B

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B/A

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A - B

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2A/B

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Solution

The correct option is D 2A/B
The correct option is D.
Given,
The potential of the particle in the force field is:

$u = \frac{A}{r^{2}} - \frac{B}{r}$

For stable in equilibrium,

$f = \frac{- d u}{d r} = 0$

$\frac{2 A}{r^{3}} + \frac{B}{r^{2}}$

$B = \frac{2 A}{B}$

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