# Flux through a Cube - Why would flux be zero?

1. Feb 15, 2009

### limonysal

1. The problem statement, all variables and given/known data
This is a three part problem. I have the first and third part down but I'm just wondering about the second part which is multiple choice.

A cube has one corner at the origin and the opposite corner at the point (L,L,L). The sides of the cube are parallel to the coordinate planes. The electric field in and around the cube is given by E = <(a+bx), c>. (im using bold for vectors)

Part A: Find the total electric flux $$\Phi$$E through the surface of the cube.
$$\Phi$$E =bL^3

Part B:
Notice that the flux through the cube does not depend on a or c. Equivalently, if we were to set b=0, so that the electric field becomes
E = <a, c>,
then the flux through the cube would be zero. Why?

a. E' does not generate any flux across any of the surfaces.
b. The flux into one side of the cube is exactly canceled by the flux out of the opposite side.
c. Both of the above statements are true.

2. Relevant equations

$$\Phi$$E=$$\int$$over the surface E*dA= EA when the field is perpendicular

3. The attempt at a solution
I feel like the flux might be canceled out but I'm not sure if it might be both or just one of th reasons.

2. Feb 15, 2009

### mikelepore

Imagine a cube-shaped region of space that happens to be in a flowing river. In a given amount of time, how much water enters one side of the space? In that same time, how much water goes out of the other side of the space? Are they equal or unequal? Would the net flow rate "in" be zero or nonzero?

3. Feb 15, 2009

### limonysal

if the water has been flowing through the cube before that instant of time, it should be the same.

If you say that b. is true, that the flux cancels, then does that contradict a. that states that there is no flux generated. But there is some generated, it just doesnt depend on x so it cancels?

i kinda feel like im trying to catch clouds here.

4. Feb 15, 2009

### limonysal

ok. so if the electric field is not dependent on x, then the flux going in through one side is the same as that going out the other end. so there is no chage in the flow rate?