A flat surface of area 3.20 m2 is rotated in a uniform electric field of magnitude e = 6.20 x 105 n/c. determine the electric flux through this area (a) when the electric field is perpendicular to the surface and (b) when the electric field is parallel to the surface.

The electric flux on a surface of area A in a uniform electric field E is given by

φ = EA cos θ

where θ = the angle between the directions of E and a normal vector to the surface of the area.

See the diagram shown below.

When the electric field is perpendicular to the surface, then θ = 0°, and

φ = EA cos (0°) = (6.20 x 10⁵ N/C) * (3.2 m²) = 1.984 x 10⁶ (N-m²) / C

When the electric field is parallel to the area, then θ = 90°, and

φ = EA cos (90°) = 0

Answer:

(a) 1.984 x 10⁶ (N-m²) / C

(b) 0