A charge q is placed at some distance along the axis of a uniformly charged disc of surface charge density $\sigma$. The flux due to the charge q through the disc is $\varphi$. The electric force on charge q exerted by the disc is

We know that if a point charge subtends a half-angle a on the circular cross-section of a disc, then flux passing through the disc is:

$\varphi =\frac{q}{2{\epsilon }_o}(1-\cos \alpha )$

Also, if a point charge q lies on the axis of a charged disc of charge density $\sigma$ and subtends a half-angle $\alpha$, then it experiences a force

$F=\frac{q\sigma }{2{\epsilon }_o}(1-\cos \alpha )=\sigma \varphi$