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A uniform electric field with a magnitude of 125000 N/C passes through a rectangle with sides of 2.50 m and 5.00 m. The angle between the electric field vector and the vector normal to the rectangular plane is 65.0°. What is the electric flux through the rectangle?

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Electric Flux is found here by definition

ϕ = ∫ E (dot) N^ dA

If area is constant - like in this rectangle,

ϕ = E (dot) N^ * A

In this equation E and N^ are vectors, and N^ is a unit vector

note: magnitude of a unit vector is by definition 1.

The dot product of them is

|E| * |N^| * cos(θ) = E * 1 * cos(θ)

SO:

ϕ = E * A * cos(θ)

ϕ = 125000 N/C * 2.5m * 5m * cos(65°) = 660341.034 N * m^2 / C

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