How Does Flux Distribute in a Gaussian Cube with a Corner Charge?

[quantum13]

Homework Statement

A particle charge of q is placed at one corner of a Gaussian cube. What multiple of $q/\epsilon_0$ gives the flux though each cube face not making up that corner?

The solution is amazing - stack up eight cubes around the corner and find the flux through each individual cube and individual face of the cube
$$(1/8 * 1/3) q/\epsilon_0 = 1/24 * q/\epsilon_0$$

However, I don't see how this makes sense. There is no charge included in the three opposite faces of the cubes meaning there should be no flux there, even though there definitely is flux from the stacked cubes method. How can this contradiction be explained?

Homework Equations

Gauss's Law

The Attempt at a Solution

Uh.. ??

 

[Delphi51]

Whew, confusing to say "q is placed at one corner of a Gaussian cube".
Leave out the word Gaussian for this cube!
The Gaussian surface you must consider is the outside surface of the set of 8 cubes surrounding q. From symmetry, you get the same flux through all the outside faces of those 8 cubes as through the three remote faces of that first cube. Looks like the Gaussian surface has 24 faces so each one gets 1/24 of the flux. And you are asked for the flux through 3 of those.

 

[tomcue]

The explanation for this apparent contradiction lies in the concept of symmetry. When using the stacked cubes method, we are essentially creating a larger Gaussian surface that includes all of the individual cube faces. This allows us to account for the flux through the opposite faces, even though there is no charge present on those faces. This is because the flux through each individual face of the cube is equal and opposite to the flux through the corresponding face on the opposite side of the cube. Therefore, when we sum up the flux through all of the individual cube faces, we are essentially canceling out the flux through the opposite faces, resulting in the correct value of 1/24 * q/\epsilon_0. This concept of symmetry is a fundamental principle in physics and is often used to simplify complex problems.