A Charge Q is distributed uniformly on a ring of radius r. A sphere of equal r is constructed with its centre at the periphery of the ring (figure 30.12) Find the flux of the electric field through the surface of the sphere.

Options

A. `(Q)/(3epsilon_(0))`
B. `(q)/(epsilon_(0))`
C. `(q)/(2epsilon_(0))`
D. zero

Answer

1

Explanation

from the geometry of the figure.`OA=OO_(1)` and `O_(1)A=O_(1)O`.thus `OAO_(1)` is equilateral triangle Hence `/_AOO_(1)=60^(@)` or `/_AOB=120^(@)`
The are `AO_(1)B` of the ring subtends an angle `120^(@)` at the centre `O`,Thus third of the ring is inside the sphere .The charge enclosed bythe sphere `=(Q)/(3)` .from Gauss'law the flux of the electric field through the surface of the sphere is `(Q)/(3epsilon_(0))`