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?

Question 1.18: 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:

 Solution -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

 

Hence, electric flux through one face of the cube i.e., through the square,

Where,

∈₀ = Permittivity of free space = 8.854 × 10⁻¹² N⁻¹C² m⁻²

q = 10 µC = 10 × 10⁻⁶ C

= 1.88 × 10⁵ N m² C⁻¹

^{Solution -2} 

 

Therefore, electric flux through the square is 1.88 × 10⁵ N m² C⁻¹.