Calculating Electric Flux Through a Rectangle with Given Electric Field

[arileah]

Homework Statement

Hello,

A 3.60cm x 4.50cm rectangle lies in the xy-plane. What is the electric flux through the rectangle if E=(80.0i + 50k) N/C ?

Homework Equations

Φ = E * A =EAcos(θ)

The Attempt at a Solution

My attempt:

First convert the rectangle units from cm to m.

4.50cm = 0.045m
3.60cm = 0.036m

Find the area of the rectangle.

A = 0.036m x 0.045m = 0.00162 m^2

Find the magnitude of the electric field.

E = sqrt (50^2 + 80^2) = 94.34 N?C (aprox.)

Multiply the two,

electric flux = E * A = 0.15283 Nm^2 / C (aprox.)

However, this answer is wrong. Could anyone point me in the right direction? I am not sure how to incorporate the cosine into this. Thank you.

 

[Doc Al]

Your error is at the point where you multiply the two: that is a vector multiplication, not a magnitude multiplication.

 

[arileah]

Thanks!