A point charge +10 μC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in the Figure. 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.)

#### Solution

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,

∈_{0} = Permittivity of free space

= 8.854 × 10^{−12} N^{−1 }C^{2 }m^{−2}

q = 10 μC = 10 × 10^{−6} C

∴ `phi = 1/6 xx (10 xx 10^-6)/(8.854 xx 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}.