(a) Define electric flux. Write its SI units.
(b) The electric field components due to a charge inside the cube of side 0.1 m are as shown:
E_x = $\mathrm{\alpha }$ x, where $\mathrm{\alpha }$ = 500 N / C^–m
E_y = 0, E_z = 0.

Calculate:
(i) the flux through the cube and
(ii) the charge inside the cube.

 

(a) Electric flux:
The total number of electric field lines crossing an area in an electric field is termed as electric flux.
It is denoted by Φ_E.
Electric flux is a scalar quantity, its SI unit is Nm² C^–1.
(b) Here, E_x = αx, E_y = 0, E_z = 0
α = 500 N/C^–m, side of a cube a = 0.1 m
As the electric field has only X-component then,

for each of four faces of cube 1 to Y-axis and Z-axis.
∴ Electric flux is only for left and right face along X-axis of cube.
(i) Electric field at the left face,

(ii) According to Gaussian law
                 
or,