Question

A point charge $Q$ is located on the axis of a disc of radius $R$ at a distance $a$ from the plane of the disc. If one fourth (1/4th) of the flux from the charge passes through the disc, the relation between $a$ and $R$ is $a=\frac{R}{\sqrt{x}}$.Find $x$.

Answer 1

solid angle subtended by ring is $2\pi (1-cos\theta )$...(i)
given the flux through the disc is 1/4th of total flux, the solid angle subtended by disc will be 1/4th of total solid angle which is $\frac{1}{4}4\pi =\pi$from equation (i)
$2\pi (1-cos\theta )=\pi \Rightarrow cos\theta =\frac{1}{2}$ from geometry $cos\theta =\frac{a}{\sqrt{a^2+R^2}}=\frac{1}{2}$
$\Rightarrow a=\frac{R}{\sqrt{3}}$
hence correct answer is 3.