A charge $Q \mu C$ is placed at the centre of a cube. The flux coming out from any one of its faces will be…
A charge $Q \mu C$ is placed at the centre of a cube. The flux coming out from any one of its faces will be (in SI unit)
$\frac{Q}{6 \varepsilon_0} \times 10^{-3}$
$\frac{Q}{6 \varepsilon_0} \times 10^{-6}$
$\frac{Q}{\varepsilon_0} \times 10^{-6}$
$\frac{2 Q}{3 \varepsilon_0} \times 10^{-3}$
Solution
According to Gauss law, total electric flux through a closed surface is
$\phi_{\text {net }}=\frac{q}{\varepsilon_0}$
$\therefore$ Total electric flux through the cube is
$\phi_T=\frac{Q \times 10^{-6}}{\varepsilon_0}$
Since charge is placed at the centre of the cube, therefore flux through each face is same.
Hence, $\phi=\frac{1}{6} \phi_T=\frac{1}{6} \times \frac{Q \times 10^{-6}}{\varepsilon_0}$
.