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Question

# A charge q is distributed uniformly on a ring of radius R. A sphere of equal radius R is constructed with its centre at the periphery of the ring, Find the flux of the electric field through the surface of the sphere

A
qϵ0
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B
q2ϵ0
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C
q3ϵ0
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D
Zero.
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Solution

## The correct option is C q3ϵ0Let point of intersection of ring & sphere are P.Q......... let center of ring is O & center of sphere is O′........OO′ bisects PQ in two equal ,if S is the point of intersection of OO′ & PQ thenIn triangle right angles POSPO=R,OS=R/2 so angle POS=θUsing trigonometry, cosθ=OS/PS=1/2θ=π/3total angle subtended by arc is 2π/3..... this is the arc of ring which lies inside sphere & substends2π/3 angle at the center of ring.....for 2π radian charge =qfor unit radian =q2πfor q2π radian q1=(q2π)(2π3)=q3total flux through sphere= total charge enclosed q3ε0∴ Option C is correct.

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