Solving Flux of Electric Field through a Cube of Side L = 2m

[ibaraku]

Homework Statement

A cube of side L = 2m is centered at the origin, with the coordinate axes perpendicular to its faces. Find the flux of the electric field E = (15N/C)i + (27N/C)j + (39N/C)k through each face of the cube

Homework Equations

phi total = (E * n) delta A

The Attempt at a Solution

Ok, so I know that
phi total = phi 1 + phi 2 + ... + phi 6

what I am confused about is how do I know where the flux is parallel to the faces of cube, where is it zero?

Thanks

 

[gabbagabbahey]

Homework Statement

A cube of side L = 2m is centered at the origin, with the coordinate axes perpendicular to its faces. Find the flux of the electric field E = (15N/C)i + (27N/C)j + (39N/C)k through each face of the cube

Homework Equations

phi total = (E * n) delta A

The Attempt at a Solution

Ok, so I know that
phi total = phi 1 + phi 2 + ... + phi 6

what I am confused about is how do I know where the flux is parallel to the faces of cube, where is it zero?

Thanks

(E*n) is the dot product between $$\vec{E}$$ and $$\hat{n}$$. You are given $$\vec{E}$$, so what is the definition of $$\hat{n}$$ for any surface? What is $$\hat{n}$$ for each surface of the cube? Once you find these, you just compute the dot product and then integrate over the area of each surface to get your phis.

 

[ibaraku]

(E*n) is the dot product between $$\vec{E}$$ and $$\hat{n}$$. You are given $$\vec{E}$$, so what is the definition of $$\hat{n}$$ for any surface? What is $$\hat{n}$$ for each surface of the cube? Once you find these, you just compute the dot product and then integrate over the area of each surface to get your phis.

Yeah I get that
[((15N/C)i + (27N/C)j + (39N/C)k] . i = (15N/C) a^2
"" "" "" "" . -i = -(15N/C) a^2
...
...

I am just wondering how do I know where one of this calculations will be zero, where will the flux be parallel to the sides of the cube, how do I recognize that?

 

[gabbagabbahey]

Yeah I get that
[((15N/C)i + (27N/C)j + (39N/C)k] . i = (15N/C) a^2
"" "" "" "" . -i = -(15N/C) a^2
...
...

I am just wondering how do I know where one of this calculations will be zero, where will the flux be parallel to the sides of the cube, how do I recognize that?

Flux is a scalar quantity...it will be neither parallel nor perpendicular to any given side. Why do you have an a^2 there? And for which face is $$\hat{n}=+\hat{i}$$?Is it the same for all faces? Can you show your whole solution?

 

[ibaraku]

What is $$\hat{i} \cdot \hat{i}$$, how about $$\hat{i} \cdot \hat{j}$$ and $$\hat{i} \cdot \hat{k}$$?

1, 0, 0

I see, so for this problem

[(15N/C)a^2 + (-15N/C)a^2 + (27N/C)a^2 + (-27N/C)a^2 + (39N/C)a^2 + (-39N/C)a^2] = 0

Thanks

 

[gabbagabbahey]

1, 0, 0

I see, so for this problem

[(15N/C)a^2 + (-15N/C)a^2 + (27N/C)a^2 + (-27N/C)a^2 + (39N/C)a^2 + (-39N/C)a^2] = 0

Thanks

If by a you mean L, then yes but you have calculated the TOTAL flux. The question asks for the flux through each side. You should draw a diagram, where you label each side and give the flux through each side.