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A point charge of $2.0\; \mu \,C$ is at the centre of a cubic Gaussian surface $9.0\; cm$ on edge. What is the net electric flux through the surface?
$4.166 \times 10^{6} \;N \;m ^{2} C ^{-1}$
$7.24 \times 10^{4} \;N \;m ^{2} C ^{-1}$
$8.34 \times 10^{5} \;N \;m ^{2} C ^{-1}$
$2.26 \times 10^{5} \;N \;m ^{2} C ^{-1}$
Solution
Net electric flux ( $\phi_{\text {Net }}$ ) through the cubic surface is given by
$\phi_{N e t}=\frac{q}{\varepsilon_{0}}$
Where, $\varepsilon_{0}=$ Permittivity of free space $=8.854 \times 10^{-12}\, N ^{-1} \,C ^{2}\, m ^{-2}$
$q =$ Net charge contained inside the cube $=2.0\, \mu \,C =2 \times 10^{-6} \,C$
$=2.26 \times 10^{5} \,N \,m ^{2} \,C ^{-1}$
$\therefore \phi_{N e t}=\frac{2 \times 10^{-6}}{8.854 \times 10^{-12}}$
The net electric flux through the surface is $2.26 \times 10^{5} \;N \;m ^{2} \,C ^{-1}$
