A charge `q_0` is distributed uniformly on a ring of radius R. A sphere of equal radius R constructed with its centre on the circumference of the ring. Find the electric flux through the surface of the sphere.

Explanation

The radius of sphere of ring are equal , join centre of ring and sphere to perimeter as shown
`C_(1) C_(2) = C_(1) A = C_(2) A = a`
`C_(1) C_(2) A` is equilateral triangle , `/_ A C_(1) B = 120^(@)` i.e. `1//3^(rd)` portion of ring is inside sphere , hence , charge inside sphere `= Q//3`.
Flux passing through sphere `= (Q//3)/(in_(0)) = (Q)/(3 in_(0))`