Question

A large sheet of uniform charge passes through a hypothetical spherical surface. The figure shows principle section of situation. The electric flux through the spherical surface is given by

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

Answer 1

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

The Gaussian surface marks a circle around the plane with radius $r^2=R^2-x^2$.

The net charge within the Gaussian surface

$q_{ence}=\sigma A=\sigma \pi r^2=\sigma \pi (R^2-x^2)$

Electric field,

$\varphi =q_{enel}/{ϵ}_0=\sigma \pi (R^2-x^2)/{ϵ}_0$