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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 one-fourth of the total electric flux from the charge passes through the disc, then choose the correct option.

A
R=3b
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B
3R=b
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C
2R=3b
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D
R=2b3
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Solution

## The correct option is A R=√3bFrom the concept of solid angle we know that, solid angle subtended by disc is 2π(1−cosθ) Since the flux through the solid angle 4π is ϕtotal=Qε0...(1) So, the flux through disc with solid angle 2π(1−cosθ) will be ϕdisc=2π(1−cosθ)Qε0(4π) ⇒ϕdisc=(1−cosθ)Q2ε0...(2) From (1) and (2) we have, ϕdisc=(ϕtotal)(1−cos θ2) ……(3) According to question, ϕdisc=14(ϕtotal) ……(4) From equation (3) and (4) we get, 14=(1−cos θ2) ⇒cosθ=12 ∴θ=60∘ From above figure, Rb=tan 60∘=√3 ∴ R=√3b Hence option (a) is correct answer.

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