A point charge q is placed at distance d from the centre of a circular disc of radiius R. Find electric flux through the disc due to that charge .

Explanation

We know that total flux original from a point charge q in all directions `(q)/(in_(0))` . This flux is originated in a solid angle 4pi . In theh given case solid angle subtended by the cone formed by the disc at the point charge is `Omega = 2pi (1-cos theta)`
So, the flux of q which is passing through the surface of the disc is .
`phi = (q)/(in_(0)) (Omega)/(4pi) = (q)/(2 in_(0)) (1-cos theta)`
From the figure , `cos theta = (d)/(sqrt(d^(2) + R^(2))) ` so `phi = (q)/(2 in_(0)) { 1- (d)/(sqrt(d^(2) + R^(2)))}`