Question

An infinitely, uniformly charged sheet with surface charge density $\sigma$ 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

• A. $\frac{\pi R^2\sigma }{{ϵ}_0}$
• B. $\frac{2\pi (R^2-x^2)\sigma }{{ϵ}_0}$
• C. $\frac{2\pi (R-x{)}^2\sigma }{{ϵ}_0}$
• D. $\frac{6\pi (R^2-x^2)\sigma }{{ϵ}_0}$

Answer 1

The correct option is D $\frac{6\pi (R^2-x^2)\sigma }{{ϵ}_0}$

The Gaussian surface marks a circle around the plane with radius :-

$r^2=R^2-x^2$

The net charge within the Gaussian surface

$q_{ene}=6A=6{\pi r}^2$

$=6\pi (R^2-x^2)$

Electric flux

$\phi =\frac{q_{ene}}{{ϵ}_0}.\frac{6\pi (R^2-x^2)}{{ϵ}_0}$