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

• limonysal
In summary, the conversation discusses a three part problem involving a cube with one corner at the origin and the opposite corner at the point (L,L,L). The electric field in and around the cube is given by E = <(a+bx), c>. The first part of the problem asks to find the total electric flux through the surface of the cube, which is expressed as \PhiE = bL^3. The second part of the problem discusses why the flux through the cube does not depend on a or c, and provides three options for the reason - 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
limonysal

## Homework Statement

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.

## Homework Equations

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

## 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.

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?

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 doesn't depend on x so it cancels?

i kinda feel like I am trying to catch clouds here.

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?

## 1. What is flux through a cube?

Flux is a measure of the flow of a physical quantity through a surface or boundary. In the case of a cube, the flux is the amount of a physical quantity passing through the surface of the cube.

## 2. How is flux through a cube calculated?

The flux through a cube is calculated by taking the dot product of the vector field and the unit normal vector of the cube's surface. This gives the amount of the vector field that is passing through the surface of the cube.

## 3. Why would flux through a cube be zero?

Flux through a cube can be zero if the dot product of the vector field and the unit normal vector is zero. This would occur if the vector field is parallel to the surface of the cube.

## 4. Can flux through a cube ever be negative?

Yes, flux through a cube can be negative if the dot product of the vector field and the unit normal vector is negative. This would occur if the vector field is pointing in the opposite direction of the surface normal.

## 5. How is flux through a cube related to Gauss's Law?

Gauss's Law states that the total flux through a closed surface is equal to the net charge enclosed by that surface. In the case of a cube, the net charge enclosed would be zero, so the total flux through the surface would also be zero.

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