# Elec. flux through the top side of a cube with q at a corner

• Pushoam
In summary, the flux through the top side of a cube can be found by taking 6 cubes of length 2a and placing the charge q at the center. Using Gauss's law and symmetry, the flux through each surface of the bigger cube is equal to ## \frac {q } {6\epsilon_0 }##. Therefore, the flux through the top side of the cube is ## \frac {q } {24\epsilon_0 }##. This result is independent of the length of the cube.
Pushoam

## Homework Statement

Find the electrix flux through the top side of a cube. The cube's corner is on the origin, and is 'a' units on length. The charge 'q' is located at the origin, with the corner of the cube.

## Homework Equations

Gauss's law and symmetry

## The Attempt at a Solution

I take 8 cubes of length 2a in such a way that the charge q is at the center.

Then, the flux through the half of the upper surface of this bigger cube is the required answer. Right?

Using Gauss's law and symmetry ,

Flux through each surface of the bigger cube is ## \frac {q } {8\epsilon_0 } ##.

Now, again using symmetry, flux through half of the surface is ## \frac {q } {16\epsilon_0 } ##, which is equal to the required answer.

Is this correct?
[/B]

Pushoam said:
Flux through each surface of the bigger cube is ## \frac {q } {8\epsilon_0 } ##.
Because? A cube has eight faces??

haruspex said:
Because? A cube has eight faces??
Sorry, it is 6.
]Flux through each surface of the bigger cube is ## \frac {q } {6\epsilon_0 }## .

Pushoam said:
Then, the flux through the half of the upper surface of this bigger cube is the required answer. Right?
The above is also wrong. It is ¼, not ½.
Now, again using symmetry, flux through ¼ of the bigger surface is ## \frac {q } {24\epsilon_0 }##, which is equal to the required answer.[/QUOTE]

Pushoam said:
Sorry, it is 6.
]Flux through each surface of the bigger cube is ## \frac {q } {6\epsilon_0 }## .The above is also wrong. It is ¼, not ½.
Now, again using symmetry, flux through ¼ of the bigger surface is ## \frac {q } {24\epsilon_0 }##, which is equal to the required answer.
[/QUOTE]
Looks right.

Thank you.
The flux is independent of the length of the cube.

## 1. What is electric flux?

Electric flux is a measure of the flow of electric field through a given surface. It is represented by the symbol Φ and is measured in units of volts per meter (V/m).

## 2. How is electric flux calculated?

Electric flux is calculated by taking the dot product of the electric field vector and the surface vector. It can also be calculated by multiplying the magnitude of the electric field by the cosine of the angle between the field and the surface.

## 3. What is the significance of having q at a corner of the cube?

Having q (the source of electric field) at a corner of the cube allows for a more complex calculation of electric flux. This is because the electric field lines will be directed at varying angles towards the surface of the cube, resulting in a non-uniform electric flux.

## 4. How does the shape of the cube affect the electric flux through the top side?

The shape of the cube can affect the electric flux through the top side because it determines the angle at which the electric field lines intersect the surface. A cube with a larger surface area will have a higher electric flux compared to a cube with a smaller surface area.

## 5. Can the electric flux through the top side of the cube be negative?

Yes, the electric flux through the top side of the cube can be negative. This occurs when the electric field lines are directed away from the surface, resulting in a negative dot product and a negative electric flux value.

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