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A Charge Q is distributed uniformly on a...

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.

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From the geometry of the figure `OA=00_1` and `O_1A=O_1 0. Thus. `OAO_1 is an equilateral triangle. Hence `angleAOO_1=60^O of angle AOB =120^0`.
The arc `AO_1B` of the ring subtends an angle `120^0` at the centre O. Thus, one third of the ring is inside the sphere. The charge enclosed by the sphere`=Q/3`. From Gauss's law, the flux of the electric field through the surface of the sphere is `Q/3epsilon_0`.
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