Physics Question from JEE Main 2023 · 11 April, Shift 1

Two equal point charges ($q_0 = + 2 \, \mu \text{C}$) are placed on a frictionless inclined plane of inclination $30^\circ$: one rests on the incline at a vertical height $h$ above the base, and the other is fixed at the bottom of the incline. Mass of each point charge is $20 \, \text{g}$. For the system of two point charges to be in equilibrium (at rest) the height $h = x \times 10^{-3} \, \text{m}$. The value of $x$ is _____.

$\left( \text{Take } \frac{1}{4\pi\epsilon_0} = 9 \times 10^{9} \, \text{N m}^2\text{C}^{-2}, \; g = 10 \, \text{ms}^{-2} \right)$