Question

A point charge +10$\mu$C is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig 1.34. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.)

Answer 1

Consider that the charge $q$ is at a distance of $5cm$ from the square $ABCD$ of each side $10cm$. Then according ti Gauss' theorem, total electric flux through all the six faces of the cube,

$\varphi =\frac{q}{{\in }_0}$

Obviously, the flux through the square $ABCD$ will be,

$\varphi =\frac{1}{6}\times \varphi =\frac{1}{6}\times \frac{q}{{\in }_0}=\frac{1}{6}\times \frac{{10}^{-5}}{8.854\times {10}^{-12}}$

$=1.88\times {10}^{5}N{m}^2{C}^{-1}$