Question

A point charge $+10\mu C$ is at a distance 5cm directly above the centre of a square of side 10cm, as shown in figure. What is the magnitude of the electric flux through the square?

Answer 1

Now, we imagine an enclosed cubical surface and the given square be one side of this cubical surface. Let the charge q is placed at the centre of cube. Now, the figure looks like
The total flux enclosed through the cube is



The flux enclosed by one face i.e., square is 1/6 of total flux (because the cube has six square shaped faces), So
The flux linked with each square
${\varphi }^{\prime }=\frac{\varphi }{6}=\frac{1}{6}.\frac{q}{{\epsilon }_0}[FromEq.(i\left)\right]{\varphi }^{\prime }=\frac{1}{6}\times \frac{10\times {10}^{-6}}{8.854\times {10}^{-12}}=1.88\times {10}^{5}N-m^2/C$
Thus, the flux linked with the square is $1.88\times {10}^{5}N-m^2/C$