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Question

# A point charge q is placed at a point on the axis of a non-conducting circular plate of radius r at a distance R(R>>r) from its center. The electric flux associated with the plate is :

A
qr24πε0R2
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B
qr24ε0R2
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C
qr24ε0r2
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D
q4ε0
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Solution

## The correct option is D q4ε0Charge =qradius =rR>>rits centre. The electric flux associated with the plate Ex on the ring of radius X=KQcosθ(b2+x2)Ex=KQb(b2+x2)3/2φ=ϕ∫Exdaφ=∫x=Rx=0KQb2πxdx(b2+x2)3/2putting x=btanθφ=2πKQbb3∫tan−1⎛⎝Rb⎞⎠0b(tanθ)bsec2θsec3θdθφ=2πKQ∫a0sinθdθ [α=tan−1√3=600]φ=2πKQ(1−cosα)φ=Q2ϵ0×12=Q4ϵ0

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