A point charge +10 μC is a distance 5 cm directly above the centreof a square of side 10 cm, as shown in Fig. 1.34. What is themagnitude of the electric flux through the square? (Hint: Think ofthe square as one face of a cube with edge 10 cm.)
Given: The magnitude of the point charge is + 10 μC , the distance of the point charge is 5 cm and the side of the square is 10 cm .
Suppose that the square is one of the faces of a cube of edge length 10 cm . The charge is placed at the centre of the cube.
Using Gauss’s theorem, the total electric flux through all six faces of cube is given as,
ϕ T = q ε 0 (1)
Where, the charge placed at the center of cube is q , the total electric flux through all six faces of the cube is ϕ T and the permittivity of the free space is ε 0 .
The magnitude of the permittivity of free space is given as,
ε 0 = 8.854 × 10 − 12 C 2 / Nm 2
The electric field through one face of the cube is given as,
ϕ = ϕ T 6 (2)
By substituting the value from equation (1) in equation (2), we get
ϕ = 1 6 q ε 0 (3)
By substituting the given values in equation (3), we get
ϕ = 1 6 10 × 10 − 6 8.854 × 10 − 12 = 1.88 × 10 5 Nm 2 / C
Thus, the magnitude of the electric flux through the square is 1.88 × 10 5 Nm 2 / C .
Given: The magnitude of the point charge is
Suppose that the square is one of the faces of a cube of edge length
Using Gauss’s theorem, the total electric flux through all six faces of cube is given as,
Where, the charge placed at the center of cube is
The magnitude of the permittivity of free space is given as,
The electric field through one face of the cube is given as,
By substituting the value from equation (1) in equation (2), we get
By substituting the given values in equation (3), we get
Thus, the magnitude of the electric flux through the square is
