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.

Options

A. `(q)/(epsilon_0)`
B. `(q)/(2epsilon_0)`
C. `(q)/(3epsilon_0)`
D. `(q)/(4epsilon_0)`

Answer

C

Explanation

Charge on ring q , centre of ring = O
Centre of sphere = O'
Linear charge density of ring `lambda = (q)/(2 pi a)`
Charge on are AB of ring ,
`q_(AB) = lambda (arc AB) = (1)/(2 pi a ) * a * (2pi )/(3)`
`q_(AB) = q//3`
`therefore` Flux coming out of sphere = `q //3 epsi_(0)` .