Question

A charge q_0 is distributed uniformly on a ring of radius R. A sphere of equal radius R constructed with its centre on the circumference of the ring. Find the electric flux through the surface of the sphere.

Answer 1

Explanation:

Let 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 then

In triangle right angles POS

PO=R,OS=R/2 so angle POS=θ

Using trigonometry, cosθ=OS/PS=1/2

θ=π/3

total angle subtended by arc is 2π/3..... this is the arc of ring which lies inside sphere & substends

2π/3 angle at the center of ring.....

for 2π radian charge =q

for unit radian = q / 2π

for q / 2π radian q1 =( q / 2π )( 2π /3 )= q / 3

total flux through sphere= total charge enclosed

= q/3ε0

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