A point charge Q is located on the axis of a disc of radius R at a distance b from the plane of the disk. If one-fourth of the electric flux from the charge passes through the disk, then $\mathrm{R}=\sqrt{\mathrm{k}}\mathrm{b}.$ Find k

Total flux associated with charge Q for solid angle $\frac{\mathrm{Q}}{{\mathrm{\epsilon }}_0}$  

Solid angle subtended by the disc at Q is

$\mathrm{\Omega }=2\mathrm{\pi }(1-\cos \mathrm{\alpha })$

$=2\mathrm{\pi }\left[1-\frac{\mathrm{b}}{\sqrt{{\mathrm{b}}^2+{\mathrm{R}}^2}}\right]$

Flux through the disc  $=\frac{\mathrm{Q\Omega }}{{\mathrm{\epsilon }}_{0}4\mathrm{\pi }}$

It is given to be $\frac{\mathrm{Q}}{4{\mathrm{\epsilon }}_0}$

So $\frac{\mathrm{Q}}{4{\mathrm{\epsilon }}_0}=\frac{\mathrm{Q\Omega }}{{\mathrm{\epsilon }}_{0}4\mathrm{\pi }}$

Solving we get $\mathrm{R}=\sqrt{3}\mathrm{b}$