Question

An infinite,uniformly charged sheet with surface charge density sigma cuts through a spherical gausian surface of radius R at a distance x from its center. The electric flux through the Gaussian surface is?

Answer 1

$Flux=\int Eds=\frac{Q_{encl}}{{\epsilon }_0}=\frac{\sigma \times \pi (R^2-x^2)}{{\epsilon }_0}=\frac{\pi \sigma (R^2-x^2)}{{\epsilon }_0}$
$\sqrt{R^2-x^2}$ is the radius of the segment of the sheet which is inside the gaussian surface.