Calculating Electric Flux Through a Rectangle

[vegeta_ban]

Homework Statement

Determine the electric flux through a 6m by 4m rectangular area. The area is oriented such that a vector normal to its surface points in the [1;6] direction. The electric field is [7;1] N/C.

Homework Equations

Φ=E·A=EA*cosθ

The Attempt at a Solution

[7;1]N/C*[24;144]m²=312 Nm²/C

I did this is wrong, right? How should i go about solving this, doesn't the electric flux equal the dot product of the electric field and the normal vector multiplied area. Am I missing something here?

 

[Dick]

Why do you think you did it wrong? It looks right to me.

 

[SammyS]

Welcome to PH Forums.

Your answer looks right !

 

[vegeta_ban]

i always second guess myself, it's a problem I missed the day we learned about EF because of a funeral and I've been playing catch up ever since.

 

[rwisz]

Your approach is correct, but your calculation is incorrect. The electric flux is a scalar quantity, so it should not have units of Nm2/C. The correct calculation would be:

Φ = E · A · cosθ = [7;1] N/C · [6;4] m2 · cos(θ)

Where θ is the angle between the electric field and the normal vector, which in this case is 90 degrees since they are perpendicular. Therefore, cos(θ) = 0 and the electric flux through the rectangle is 0.

In general, the electric flux through a surface is given by the formula Φ = ∫∫E · dA, where the integral is taken over the entire surface. In this case, since the electric field is constant over the entire surface, the integral simplifies to Φ = E · A, which is what you used in your calculation.