A uniform surface charge density 8$\mathrm{\sigma }$ exists over the entire x-y plane except for a circular hole of radius a centered at the origin. The electric field at a point $\mathrm{P}\left(0,0,\sqrt{3}\mathrm{a}\right)$ on the z- axis is found to be $\sqrt{\mathrm{x}}\frac{\mathrm{\sigma }}{{\mathrm{\epsilon }}_0}$. Find the value of x.