The potential energy of a particle in a certain field has the form `U=(a//r^2)-(b//r)` , where a and b are positive constants and r is the distance from the centre of the field. Find the value of `r_0` corresponding to the equilibrium position of the particle, examine whether this position is stable.

Explanation

To find the equilibrium position \( r_0 \) of a particle in the given potential energy field \( U = \frac{a}{r^2} - \frac{b}{r} \), we need to follow these steps:

### Step 1: Find the Force
The force \( F \) acting on the particle is given by the negative gradient of the potential energy:
\[ F = -\frac{dU}{dr} \]
First, we differentiate \( U \) with respect to \( r \).
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