Question

A charge q is distributed uniformly on a ring of radius r speed of equal radius r is centred at the sun become friends of the ring find the flux of the electric field to the surface of the screen

Answer 1

Answer:

Explanation:

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 = θ

using trigonometry , cosθ = OS/PS = 1/2

θ = π/3

total angle substended 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 2π/3 radian q1 = (q/2π)(2π/3) = q/3

total flux through sphere = total charge enclosed/ε₀= q/3ε₀

this is the required flux