Answer
$\phi=3.01n\frac{N.m^2}{C}$
Work Step by Step
If we think the square as one face of a cube then the flux through the square will be $\frac{1}{6}$ of the total flux through the cube i.e.
$\phi=\frac{\phi_{total}}{6}$
According to Gauss's law, the flux through a closed surface is given as:
$\phi_{total}=\frac{q}{\epsilon_{\circ}}$
We plug in the known values to obtain:
$\phi_{total}=\frac{1.6\times 10^{-19}}{8.85\times 10^{-12}}=1.8079\times 10^{-8}\frac{N.m^2}{C}$
Now,
$\phi=\frac{\phi_{total}}{6}=\frac{1.8079\times 10^{-8}}{6}=3.01\times 10^{-9}\frac{N.m^2}{C}=3.01n\frac{N.m^2}{C}$
