How Much Flux Passes Through a Square in a Non-Uniform Electric Field?

[justin15501]

Homework Statement

Consider an electric field E = 2x i - 3y j. The coordinate x and y are measured in meters and the electric field is in N/C. What is the magnitude of the flux of this field through a square whose corners are located at (x,y,z) = (0,2,0), (2,2,0), (2,2,2), (0,2,2)?

Homework Equations

Our proffesor gave us the answer of 24. He's been wrong before so I'm not sure. The choices are 6, 12, 24, 0, 48.

The Attempt at a Solution

https://gyazo.com/bb9e4506b7124f7704ab9e0393f6d7f8
I did this in math cad. I've never done double integrals and I need some help. Thanks!

 

[SammyS]

Homework Statement

Consider an electric field E = 2x i - 3y j. The coordinate x and y are measured in meters and the electric field is in N/C. What is the magnitude of the flux of this field through a square whose corners are located at (x,y,z) = (0,2,0), (2,2,0), (2,2,0), (0,2,2)?

Homework Equations

Our proffesor gave us the answer of 24. He's been wrong before so I'm not sure. The choices are 6, 12, 24, 0, 48.

The Attempt at a Solution

https://gyazo.com/bb9e4506b7124f7704ab9e0393f6d7f8
I did this in math cad. I've never done double integrals and I need some help. Thanks!

Here is your Math Cad image:

It looks like your square only has 3 corners. I suppose the missing corner is at (2,2,2).

What is the definition of flux? It should include a scalar product (dot product).

 

[justin15501]

Here is your Math Cad image:
View attachment 103440

It looks like your square only has 3 corners. I suppose the missing corner is at (2,2,2).

What is the definition of flux? It should include a scalar product (dot product).

I edited the original post. Sorry, I miss typed! It is at (2,2,2).
The definition of flux is the integral of electric field doted with area. What am I doing wrong in mathcad?

 

[SammyS]

I edited the original post. Sorry, I miss typed! It is at (2,2,2).
The definition of flux is the integral of electric field doted with area. What am I doing wrong in mathcad?

What is the normal vector to the area ?

 

[justin15501]

What is the normal vector to the area ?

Would the normal vector be flux? I'm not sure.

 

[SammyS]

Would the normal vector be flux? I'm not sure.

No. You need a vector to associate with the area, so that you can take the dot product of that vector and the electric field.

The surface of the square is parallel to the x-z plane. What unit vector is normal to that square?

 

[justin15501]

No. You need a vector to associate with the area, so that you can take the dot product of that vector and the electric field.

The surface of the square is parallel to the x-z plane. What unit vector is normal to that square?

j? I'm not searching for someone to do the problem for me, but I'm pressed for time as we were given this extra credit assignment today, so if you could just solve this and explain the steps you took, I would really appreciate it. The only reason I am asking is because of my time constraint.

 

[justin15501]

I get that the flux goes through the j hat direction, so you take (3*2) = 6 and then multiply it by the area (2*2) and get 24. But my teacher wants us to solve this using a double integral in math cad for bonus points. I've never done double integrals so I just need an example or someone to do it and show me how..

 

[SammyS]

j? I'm not searching for someone to do the problem for me, but I'm pressed for time as we were given this extra credit assignment today,

so if you could just solve this and explain the steps you took, I would really appreciate it. The only reason I am asking is because of my time constraint.

That's a self contradictory statement.

It's against PF rules to provide you with a solution. The best we can do is to help you to solve this yourself.

I get that the flux goes through the j hat direction, so you take (3*2) = 6 and then multiply it by the area (2*2) and get 24. But my teacher wants us to solve this using a double integral in math cad for bonus points. I've never done double integrals so I just need an example or someone to do it and show me how..

How do you describe the area over which you integrate? ... in addition to being normal to $\ \hat{j}\$