An electric field $$\vec{E} = (2x\hat{i}) \text{ NC}^{-1}$$ exists in space. A cube of side $$2 \text{ m}$$ is placed in the space as per figure given below.

The electric flux through the cube is ______ $$\text{Nm}^2/\text{C}$$.

Given

$$E⃗=(2x)x$$

Cube side:

a=2m

From figure, cube extends from

x=2

to

x=4

Only two faces perpendicular to x-axis contribute flux, because field is along x-direction.

At left face:

x=2

$$E_1=2(2)=4$$

Area of face

$$A=2\times2=4$$

Flux through left face (inward, negative):

$$\Phi_1=-E_1A$$

$$=-4(4)=-16$$

At right face:

x=4

$$E_2=2(4)=8$$

Flux through right face:

$$\Phi_2=E_2$$

$$=8(4)=32$$

Net flux

$$\Phi=\Phi_1+\Phi_2$$

$$=32-16$$

$$=16$$