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A point charge Q is located on the axis ...

A point charge Q is located on the axis of a disc of radius R at a distance b from the plane of the disc (figure). Show that if one-fourth of the electric flux from the charge passes through the disc, then `R=sqrt3b`.

Text Solution

Verified by Experts

The correct Answer is:
`sqrt(3) b`
Solid angle subtended by disk at Q is
`Omega = 2pi(1-cosalpha)`
`=2pi[1-b/(sqrt(b^2+R^2))]`
Flux through disk is `(QOmega)//(epsilon_04pi)`
It is given to be `Q//4epsilon_0`.
So, `Q/(4epsilon_0) = (QOmega)/(epsilon_04pi)`
Solve to get R `= sqrt(3)b`.
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