Question

A point charge Q is located on the axis of a disk of radius R at a distance b from the plane of the disk. Show that if one-fourth of the electric flux from the charge passes through the disk, then `R = sqrt(3b)`.

Answer 1

Correct Answer - `sqrt(3) b`
Solid angle subtended by disk at Q is
`Omega = 2pi(1-cosalpha)`
`=2pi[1-b/(sqrt(b^2+R^2))]`
Flux through disk is `(QOmega)//(epsilon_04pi)`
It is given to be `Q//4epsilon_0`.
So, `Q/(4epsilon_0) = (QOmega)/(epsilon_04pi)`
Solve to get R `= sqrt(3)b`.