A point charge Q is located on the axis of a disc of radius R at a distance a from the plane of the disc. If one fourth(1/4th) of the flux from the charge passes through the disk, then find the relation between a and R..
With the point charge as the center construct a sphere of radius R2+a2 so that the boundary of the plate lies on the sphere. Total flux through this sphere is = q/
Then the solid angle subtended by the plate at the point charge is = 2(1-cos) where is the semi vertical angle of the cone formed by the plate at the point charge. cos = a/ R2+a2
Now, a solid angle of 4 contains a flux q/ Hence a solid angle of 2(1-cos) contains flux [(q/)/4]2(1-cos) =(q/2)(1-cos) =(q/2)(1-a/ R2+a2)
As per the question, (1/4)(q/) = (q/2)(1-a/ R2+a2) a = R/ 3
Moderation Team
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R2+a2 so that the boundary of the plate lies on the sphere.
= q/
(1-cos
)
R2+a2)
