Question

A point charge of $2\mu c$ is placed at the center of a cubic Gaussian surface of side $0.5cm$. What is the net flux through the surface?
(Given ${\epsilon }_0=8.85\times {10}^{-12}{C}^2/N/m^2$).

Answer 1

Given - $q=2\mu C=2\times {10}^{-6}C$

Let ${\varphi }_E$ be the flux passing through any one face of the cube . As all 6 faces of cube are symmetrical to point charge at center , therefore flux through any surface will be ${\varphi }_E$ . Hence total flux through the cube will be $6{\varphi }_E$ .

By Gauss' theorem

$6{\varphi }_E=q/{\epsilon }_0$

or ${\varphi }_E=q/6{\epsilon }_0=2\times {10}^{-6}/8.85\times {10}^{-12}=2.25\times {10}^{5}N-m^2/C$