A square surface measures 4.4 mm on each side. It is immersed in a uniform electric field with magnitude E = 2100 N/C and with field lines at an angle of 35° with a normal to the surface. Take that normal to be "outward," as though the surface were one face of a box. Calculate the electric flux through the surface.

To calculate the electric flux through the surface, we can use the formula:

Φ = E * A * cos(θ)

Where:
Φ is the electric flux,
E is the magnitude of the electric field,
A is the area of the surface, and
θ is the angle between the electric field lines and the normal to the surface.

In this case, we are given:
E = 2100 N/C (magnitude of the electric field)
A = (length of one side of the square surface)^2 = (4.4 mm)^2
θ = 35° (angle between field lines and normal)

We need to convert the given length from millimeters (mm) to meters (m) since the electric field is given in newtons per coulomb (N/C) which is the SI unit.

1 mm = 1/1000 meters (conversion factor)

Converting the length from mm to meters:
Side length = 4.4 mm * (1/1000) meters/mm = 0.0044 meters

Now we can calculate the area:
A = (0.0044 meters)^2 = 1.936 * 10^(-5) square meters

Next, we can substitute the values into the formula to calculate the electric flux:

Φ = E * A * cos(θ)
Φ = (2100 N/C) * (1.936 * 10^(-5) square meters) * cos(35°)

Using a calculator, we can compute the value of the electric flux.