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

Explanation

We know that total flux originated from a point charge q in all directions is `(q)/(in_(0))`. This flux is originated in a solid angle `4pi`. In the given case solid angle subtended by the cone subtended 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)/(2in_(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)))}`