# A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge.

Question:

A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?

Solution:

Net electric flux $\left(\Phi_{\text {Net }}\right)$ through the cubic surface is given by,

$\phi_{\text {Net }}=\frac{q}{\epsilon_{0}}$

Where,

$\epsilon_{0}=$ Permittivity of free space

$=8.854 \times 10^{-12} \mathrm{~N}^{-1} \mathrm{C}^{2} \mathrm{~m}^{-2}$

$q=$ Net charge contained inside the cube $=2.0 \mu \mathrm{C}=2 \times 10^{-6} \mathrm{C}$

$\therefore \phi_{\text {Net }}=\frac{2 \times 10^{-6}}{8.854 \times 10^{-12}}$

$=2.26 \times 10^{5} \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-1}$

The net electric flux through the surface is $2.26 \times 10^{5} \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-1}$.