An infinite, uniformly charged sheet with surface charge density σ cuts through a spherical Gaussian surface of radius R at a distance x from its center, as shown in the figure. The electric flux through the Gaussian surface is :
πR2σϵ0
2π(R2−x2)ϵ0
π(R2−x2)σϵ0
π(R−x)2σϵ0
A
πR2σϵ0
B
π(R2−x2)σϵ0
C
2π(R2−x2)ϵ0
D
π(R−x)2σϵ0
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Solution
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Applying Gauss's law, electric flux,ϕ=Qenclosedϵ0
Here charge enclosed by Gaussian surface, Qenclosed=π(R2−x2)σ
So, electric flux through the Gaussian surface, ϕ=π(R2−x2)σϵ0
Ans:(D)
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