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The electric field components in the figure shown is non-uniform and given by px along x-axis only. The flux through the cube of edge 0.1 m is about (
Question

The electric field components in the figure shown is non-uniform and given by px along x-axis only. The flux through the cube of edge 0.1 m is about (p = 1000 N C⁻¹ m⁻¹)

A.

4.5 N m² C⁻¹

B.

3.2 N m² C⁻¹

C.

0

D.

1.3 N m² C⁻¹​

Correct option is B

Correct answer is B
Concept:
The electric flux through a surface is given by:
Φ = ∫ E ⋅ dA
In this case, the electric field is non-uniform and varies as Ex = p√x along the x-axis.
Explanation:
The cube has an edge length of 0.1 m. The area of one face is:
A = (edge)2 = 0.1 × 0.1 = 0.01 m2
The electric field at the left face  (x = 0.1):
Ex2 = p√x = 1000√0.1 = 1000 × 0.316 = 316 N/C
Flux through the left face:
Φright = Ex2 × A = 316 × 0.01 = 3.16 N·m2/C
Total flux through the cube:
Φ = Φleft = 3.16 N·m2/C

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