Flux Due to an Electric Field:

Definition:
The flux due to an electric field through a surface is a measure of the total number of electric field lines passing through that surface.

Formula:
The flux due to an electric field E passing through a surface A is given by the formula:
Flux (Φ) = E * A * cos(θ)
where E is the magnitude of the electric field, A is the area of the surface, and θ is the angle between the electric field and the normal to the surface.

Given:
Electric field E = 3 × 10^3 i N/C
Side of the square = 10 cm (0.1 m)

Calculating Area:
The area of a square can be calculated using the formula:
Area (A) = side * side
= 0.1 m * 0.1 m
= 0.01 m^2

Calculating Flux:
Since the electric field is normal to the square, the angle θ between the electric field and the normal to the surface is 0 degrees. Therefore, cos(θ) = cos(0) = 1.
Using the formula for flux, we can calculate:
Flux (Φ) = E * A * cos(θ)
= (3 × 10^3 N/C) * (0.01 m^2) * 1
= 30 Nm^2/C

Explanation:
The flux due to an electric field passing through a surface is a measure of the total number of electric field lines passing through that surface. In this case, the electric field E = 3 × 10^3 i N/C is passing through a square with a side of 10 cm. The area of the square is calculated to be 0.01 m^2.

Since the electric field is normal to the square, the angle θ between the electric field and the normal to the surface is 0 degrees. Therefore, cos(θ) = cos(0) = 1.

Using the formula for flux, Flux (Φ) = E * A * cos(θ), we substitute the given values and calculate the flux to be 30 Nm^2/C.

Conclusion:
The flux due to the given electric field passing through the square is 30 Nm^2/C.