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 . If ¼ th of the electric flux from the charge passes through the disc, then show that R=sqrt(3b).

Question

​​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 . If ¼ th of the electric flux from the charge passes through the disc, then show that R=sqrt(3b).

Sumit Majumdar · Answer

Draw a sphere whose center is at a distance b from the disk and which cover the disk

we know that flux throug a segment which makes an angel θ at the center is

Φ=Q/2ε (1-cosθ)

where cosθ = b/(b2+r2)1/2

given flux passes in 1/4 th

so Q/2ε (1-cosθ) =Q/4ε

1-cosθ = 1/2

cosθ =1/2

b/(b2+r2)1/2=1/2

r =√3 b

Regards

Sumit

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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 . If ¼ th of the electric flux from the charge passes through the disc, then show that R=sqrt(3b).

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 . If ¼ th of the electric flux from the charge passes through the disc, then show that R=sqrt(3b).

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​​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 . If ¼ th of the electric flux from the charge passes through the disc, then show that R=sqrt(3b).

​​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 . If ¼ th of the electric flux from the charge passes through the disc, then show that R=sqrt(3b).

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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 . If ¼ th of the electric flux from the charge passes through the disc, then show that R=sqrt(3b).

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 . If ¼ th of the electric flux from the charge passes through the disc, then show that R=sqrt(3b).