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let point of intersection of ring & sphere are P,Q ...let center of ring is C & center of sphere is C1 ...
CC1 bisects PQ in two equal parts , if S is the point of intersection of CC1 & PQ then
in triangle right angled PCS
PC = R , CS = R/2 so angle PCS = @
using trigonometry , cos@ = CS/PS = 1/2
@ = pi/3
total angle substended by arc is 2pi/3...this is the arc of ring which lies inside sphere & substends
2pi/3 angle at the center of ring...
for 2pi radian charge = q
for unit radian = q/2pi
for 2pi/3 radian q1 = (q/2pi)(2pi/3) = q/3
total flux through sphere = total charge enclosed/o = q/3o
this is the required flux
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