Calculating Electric Flux Through a Cube with a Non-Uniform Electric Field

[Oblivion77]

Homework Statement

Homework Equations

E * A

The Attempt at a Solution

I need to find the electric flux through each face. I am a bit confused. I believe the flux through sides 3 and 1 are zero because those sides are parallel to the electric field. The whole flux through the cube should be 0, I am not sure how to find the electric flux through the other sides because the electric field has 2 components.

 

[LowlyPion]

You might want to consider this:
http://hyperphysics.phy-astr.gsu.edu/hbase/intare.html#c1

To find the flux you will be needing to consider the angle of the field vectors through the surface.

 

[Oblivion77]

Would the angle be Tan(3.27/5.20) for the electric field?

 

[Oblivion77]

Ok, if I start to write out the area vectors I get.

A1 = -L$$^{2}$$j
A2 = L$$^{2}$$k
A3 = L$$^{2}$$j
A4 = -L$$^{2}$$k
A5 = L$$^{2}$$i
A6 = -L$$^{2}$$i

Now I need to multiple these by the electric field, what is the best way to do it?

 

[Oblivion77]

anyone?

 

[Brian_C]

Use the definition of flux. It is the dot product of the electric field and the outwardly directed area vector. Since the electric field is non-uniform, you will need to do a little calculus. You should notice that the x-coordinate is constant on two faces, and the z-coordinate is constant on two faces.

 

[Oblivion77]

I am still confused, I haven't really done a problem before with a non-uniform electric field. My textbook doesn't really have any good examples of this.

 

[Oblivion77]

Ahhh, I think I understand it now.