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Question

An infinitely, uniformly charged sheet with surface charge density σ cuts through a spherical Gaussian surface of radius R at a distance x from the centre, as shown.The electric flux through the Gaussian surface is
597001_e2473e27a6744c83b14e5ec272da8bee.png

A
πR2σϵ0
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B
2π(R2x2)σϵ0
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C
2π(Rx)2σϵ0
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D
6π(R2x2)σϵ0
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Solution

The correct option is D 6π(R2x2)σϵ0

The Gaussian surface marks a circle around the plane with radius :-
r2=R2x2
The net charge within the Gaussian surface
qene=6A=6πr2
=6π(R2x2)
Electric flux
φ=qeneϵ0.6π(R2x2)ϵ0

1233314_597001_ans_73e273b4c1e74e67a28fbdcad82745a7.jpg

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