Question

A charge `q` is placed at the some distance along the axis of a uniformly charged disc of surface cahrge density `sigma`. The flux due to the charge `q` through the disc is `phi`. The electric force on charge `q` exerted by the disc is
A. `sigma phi`
B. `(sigma phi)/(4pi)`
C. `(sigma phi)/(2pi)`
D. `(sigma phi)/(3 pi)`

Answer 1

Correct Answer - a
We know that if a point charge subtends a half-angle `alpha` on the circular cross-section of a disc, then flux passing through the disc is :
`phi=(q)/(2 epsilon_(0))(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-anlge `alpha`, then it experiences a force
`F= (q sigma)/(2 epsilon_(0))(1-cos alpha)= sigma phi`