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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).
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
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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