Question

A point charge \(+10 µC\) 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

The square can be considered as one face of a cube of edge 10 cm with a centre where charge q is placed. According to Gauss’s theorem for a cube, total electric flux is through all its six faces. 
\(Φ_{Total }= \frac{q}{ε_0}\)
Hence, electric flux through one face of the cube i.e., through the square is
                           \(  Φ= \frac{Φ_{Total}}{6} = \frac{1}{6}.\frac{q}{ε_0}\)
Where, 
\(ε_0 \)= Permittivity of free space \(= 8.854 × 10^{−12} N^{−1}C^2 m^{−2}\)
\(q = 10 µC = 10 × 10^{−6} C\)
\(Φ = \frac{1}{6}.\frac{10 × 10^{-6}}{68.854 × 10^{-12}}\)
\(= 1.88 × 10^5 N m^2 C^{−1}\)
Therefore, electric flux through the square is \(= 1.88 × 10^5 N m^2 C^{−1}.\)