An infinite, uniformly charged sheet with surface charge density `sigma` cuts through a spherical Gaussian surface of radius `R` at a distance `X` from its center, as shown in the figure. The electric flux `Phi` through the Gaussian surface is .

Options

A. `(pi R^(2) sigma)/(epsi_(0))`
B. `(2 pi(R^(2) - x^(2))sigma)/(epsi_(0))`
C. `(x (R-x)^(2) sigma)/(epsi_(0))`
D. `(x(R^(2) - x^(2))sigma)/(epsi_(0))`

Answer

D

Explanation

Area of sheet Gaussian surface `=pi (R^2-x^2`
Charge `=sigma pi (R^2-x^2)`, Flux `=(q_(in))/e_0=(sigma pi (R^2-x^2))/e_0`