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A charge q is distributed uniformly on a ring of radius R.A sphere of equal radius R is constructed with its centre on circumference of ring.Find electric flux through surface of sphere.Explanation is must.....
let point of intersection of ring & sphere are P,Q ...let center of ring is O & center of sphere is O1 ...
OO1 bisects PQ in two equal parts , if S is the point of intersection of OO1 & PQ then
in triangle right angled POS
PO = R , OS = R/2 so angle POS = @
using trigonometry , cos@ = OS/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/ebsilen = q/3ebsilen
this is the required flux
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