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

Explanation

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.
`phi_(Total)=(q)/(in_(0))`
Hence, electric flux through one face of the cube i.e., through the square, `phi=(phi_(Total))/(6)`
`=(1)/(6)(q)/(in_(0))`
Where,
`in_(0)` = Permittivity of free space
`=8.854xx10^(-12)N^(-1)C^(2)m^(-2)`
`q=10muC=10xx10^(-6)C`
`thereforephi=(1)/(6)xx(10xx10^(-6))/(8.854xx10^(-12))`
`=1.88xx10^(5)Nm^(2)C^(-1)`
Therefore, electric flux through the square is `1.88xx10^(5)Nm^(2)C^(-1)`.