Calculate flux through face of a cube

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In summary, the problem involves finding the electric flux through a shaded face at y=L due to a point charge q located at the corner of a cube with edges of length L. Using Gauss's Law, it is determined that the flux through the original face is q/(24ε). This is confirmed to be the correct solution in the solution manual.
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Homework Statement



A point charge q is located at the corner of a cube with edges of length
L. Find the electric flux through the shaded face at y = L.

Homework Equations



Gauss's Law; flux = ∫E[itex]\bullet[/itex]n dA = qenc

The Attempt at a Solution



Here's what I'm thinking. In the problem statement, the charge q is located at a corner of the cube. I can't use Gauss's Law, due to lack of symmetry. However, I can draw a bigger cube instead, whose center is at the location of the charge. Then I have symmetry to use Gauss's law and say that the flux through the whole cube is q/ε. The face whose flux the problem wants me to calculate is now just 1/24 of the surface area of the whole (bigger) cube. Therefore I can say that the flux through the original face is just q/(24ε).

Is this correct, or am I just trying to be too clever by half, as they say?
 
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  • #2
This is correct and in fact is the manner in which the problem is solved in the solution manual. Good job!
 
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  • #3
Nice! Seemed a bit too good to be true. :)
 

FAQ: Calculate flux through face of a cube

What is flux?

Flux is a measure of the flow of a physical quantity through a surface. It can also be described as the amount of a physical quantity passing through a surface per unit time.

What is the face of a cube?

The face of a cube is one of the six flat surfaces that make up a cube. It is a square and has equal length and width.

How do you calculate the flux through the face of a cube?

The flux through the face of a cube can be calculated by multiplying the magnitude of the physical quantity passing through the surface by the area of the surface. This can be represented mathematically as Φ = A ⋅ Q, where Φ is the flux, A is the area of the face, and Q is the physical quantity passing through the face.

What is the unit of flux?

The unit of flux depends on the physical quantity being measured. For example, if the physical quantity is electric field, the unit of flux would be volts per meter. If the physical quantity is magnetic field, the unit of flux would be webers (or tesla-meters) per square meter.

Can the flux through the face of a cube be negative?

Yes, the flux through the face of a cube can be negative if the physical quantity passing through the surface is directed in the opposite direction of the normal vector of the surface. This indicates that the flow is leaving the surface rather than entering it.

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