A uniform electric field of magnitude 2.80×10 ^4 N/C makes an angle of 37 degrees with a plane surface of area 1.40×10−2 m^2.

A)What is the electric flux through this surface? N * m^2/C

To calculate the electric flux through a surface, we need to use the formula:

Electric Flux (Φ) = Electric Field (E) * Area (A) * cos(θ)

Where:
- Electric Field (E) is the magnitude of the electric field vector.
- Area (A) is the area of the surface.
- θ is the angle between the electric field vector and the surface.

In this case, we are given:
- Electric Field (E) = 2.80×10^4 N/C
- Area (A) = 1.40×10^(-2) m^2
- θ = 37 degrees

Substituting these values into the formula, we get:

Electric Flux (Φ) = (2.80×10^4 N/C) * (1.40×10^(-2) m^2) * cos(37 degrees)

To find the cos(37 degrees), we can use a calculator or refer to a trigonometry table. The cosine of 37 degrees is approximately 0.7986.

Electric Flux (Φ) = (2.80×10^4 N/C) * (1.40×10^(-2) m^2) * 0.7986

Now, we can perform the calculation to find the electric flux:

Electric Flux (Φ) = 3.94944 N * m^2/C

Therefore, the electric flux through the given surface is approximately 3.94944 N * m^2/C.