How do you calculate the total E-field for a cube with a 3D vector E-field?

[dillonmhudson]

I have a cube with sides l and therefore a total volume of l^3. The E-field is ax + by + cz where a, b, and c are known constants. It says to find the total E-field. The answer is (a + b + c)*l^3. I have no idea how they get this. I tried summing up all of the sides separately bit I kept getting zero. I understand why it is zero and do not understand the answer in the book. How do you do it? Thanks for the help!

 

[kuruman]

I have a cube with sides l and therefore a total volume of l^3. The E-field is ax + by + cz where a, b, and c are known constants.

The direction of the electric field is very important. What is that direction?

It says to find the total E-field. The answer is (a + b + c)*l^3. I have no idea how they get this. I tried summing up all of the sides separately bit I kept getting zero. I understand why it is zero and do not understand the answer in the book. How do you do it? Thanks for the help!

I thought you knew what the E-field is. What does "it" really say you should find?

 

[dillonmhudson]

Sorry my mistake. It says to find the total flux through the cube. The direction of the E-field is simply the function i gave you with positive x, y, and z axes.

 

[kuruman]

Sorry my mistake. It says to find the total flux through the cube. The direction of the E-field is simply the function i gave you with positive x, y, and z axes.

The function you posted appears to be a scalar function with no direction attached to it.

 

[ideasrule]

Oh, so it has component a is the x direction, component b in the y direction, and component c in the z direction? If that's the case, then I agree, total flux has to be zero.

 

[dillonmhudson]

ax (positive x) + by (positive y) + cz (positive z)
apex is at (0,0,0)
another apex at (L,0,0) & (0,L,0) & (0,0,L) etc.

 

[ideasrule]

Now we're getting somewhere. Try calculating the flux in each direction (x,y,z), then adding them together vectorially to get the answer.

 

[kuruman]

ax (positive x) + by (positive y) + cz (positive z)
apex is at (0,0,0)
another apex at (L,0,0) & (0,L,0) & (0,0,L) etc.

I guess you mean

$$\vec{E}=ax\hat{x}+by\hat{y}+cz\hat{z}$$

As ideasrule said, calculate the flux through each face separately, remembering that the normal to the surface is always outward.

 

[dillonmhudson]

And that's when I get zero

 

[kuruman]

Can you show exactly how you get zero? Consider the two faces at x = +l and x = -l.

 

[dillonmhudson]

sorry the corner is at the origin. I got it. I wasn't plugging in the coordinates once I integrated. Three of the sides have a flux of zero b/c they lie on some line. Thanks for the help and sorry for being so confusing!