Flux Calculation for Non-Uniform Electric Field on Cube Sides

[Melawrghk]

Homework Statement

A cube has sides of length L = 0.370 m. It is placed with one corner at the origin. The electric field is not uniform but is given by E=-4.33xi+2.32zk.
Find flux through every side of the cube.

Homework Equations

Flux=EA

The Attempt at a Solution

There is no y-component to E, so I figured there wouldn't be any flux through the sides perpendicular to the y-axis.
For those faces perpendicular to x-axis:
the field is pointing left, so for the face on the left, the flux would be positive (it's leaving the face) and for face on the right, the flux would be negative (it's entering the face).
Flux (left face) = (0.37^2)*4.33=0.593

I used similar approach for all other faces, but that's wrong. Then I saw that it's -4.33x *i. So does that mean I have to multiply by 0.37 again? Because that's apparently wrong too.

Thanks, help will be really appreciated.

 

[Doc Al]

I assume the sides of the cube are parallel to the axes.

The Attempt at a Solution

There is no y-component to E, so I figured there wouldn't be any flux through the sides perpendicular to the y-axis.

Good.

For those faces perpendicular to x-axis:
the field is pointing left, so for the face on the left, the flux would be positive (it's leaving the face) and for face on the right, the flux would be negative (it's entering the face).
Flux (left face) = (0.37^2)*4.33=0.593

What's the x coordinate of that left face? What's the field? (Same questions for the right face.)

I used similar approach for all other faces, but that's wrong. Then I saw that it's -4.33x *i. So does that mean I have to multiply by 0.37 again?

It means that the field depends on the value of the x coordinate.

 

[Melawrghk]

Coordinate of the x-face? Well, it stretches from 0 to 0.37, should I integrate for all values?

 

[Doc Al]

Coordinate of the x-face? Well, it stretches from 0 to 0.37, should I integrate for all values?

The x-coordinate of the two faces that are perpendicular to the x-axis. You need it to find the field. No need to integrate.

 

[Melawrghk]

Oh I see. So like, in my case, the two faces will intersect the x-axis at 0 and 0.37, so I put those values in?

 

[Doc Al]

So like, in my case, the two faces will intersect the x-axis at 0 and 0.37, so I put those values in?

Yes.

 

[Melawrghk]

Awesome, thanks!