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

Approved