Question

A flat surface with area 0.14m^2 lies in the x-y plane, in a uniform electric field given by E= 5.1i^+2.1j^+3.5k^ kN/C. find the flux through this surface

Answer 1

Flux =∫E dA = E·A = EA cos(θ)

Since the surface lies in the xy-plane, it's area vector is pointed in the z-direction, so only the z-component of the electric field contributes tothe flux.

Flux =E·A =(5.1, 2.1, 3.5)kN/C · (0, 0, 0.14) m²= 490. N m² / C

Answer 2

Since it is in the x-y plane, we can ignore the i and j components; the k isthe only one that is normal to the plane. So the flux is simple:

(3.5 N/C)(0.14 m²) = 0.49 Nm²/C