What is the Flux Through Each Face of a Cube with a Corner Point Charge?

  • Thread starter Ed Aboud
  • Start date
  • Tags
    Cube Flux
In summary, the conversation discusses the use of Gauss's Law and symmetry arguments to determine the flux through each face of a cube with a point charge placed at one corner. The answer is found to be 6q/ε0, as the total flux through the cube is simply the charge itself divided by the electric constant. The solution does not require integration, only a consideration of symmetry.
  • #1
Ed Aboud
201
0

Homework Statement



A point charge q is placed at one corner of a cube of edge a. What is the flux through each of the cube faces?


Homework Equations





The Attempt at a Solution



I drew a diagram of the situation. I'm pretty sure that I should use Gauss' Law and some symmetry arguments but I am not sure how to integrate over the cubes faces taking into account that the electric field produced by the point charge is radially outwards, like a sphere cutting through the face of the cube ( poorly described I know, sorry).

Thanks for the help.
 
Physics news on Phys.org
  • #2
By Gauss's Law, the flux through the whole cube is just [tex] 6q/\epsilon_0 [/tex]. Now, apply a simple symmetry argument to get the answer.
 
  • #3
I'm not sure why is it 6q ? If there is only one charge of magnitude 1q surely the flux is

[tex]
q/\epsilon_0
[/tex]
 
  • #4
Right: The total flux from that charge is just q/ε0. So what's the total flux through the cube? Through each face of the cube? (No integration needed, just symmetry.)
 
  • #5
Ah right I see now. Thanks very much, was thinking about this completely the wrong way.
 
  • #6
Ed Aboud said:
Ah right I see now. Thanks very much, was thinking about this completely the wrong way.

So...
What is the answer you are getting?
 

FAQ: What is the Flux Through Each Face of a Cube with a Corner Point Charge?

What is flux through each face on a cube?

The flux through each face on a cube is a measure of the flow of a quantity (such as electric field or fluid velocity) through the surface of the cube. It is represented by the symbol Φ and is measured in units of, for example, volts or cubic meters per second.

How is the flux through each face on a cube calculated?

The flux through each face on a cube is calculated by taking the dot product of the vector field (representing the quantity) and the normal vector to the surface of the cube. This calculation can be done for each face of the cube and then summed to get the total flux through the entire cube.

What factors affect the flux through each face on a cube?

The flux through each face on a cube is affected by the magnitude and direction of the vector field, as well as the orientation and size of the cube. It may also be affected by external factors such as boundaries or other objects in the surrounding environment.

How is the flux through each face on a cube related to the divergence of the vector field?

The flux through each face on a cube is directly related to the divergence of the vector field. The divergence represents the net flow of the vector field out of a given point, and the flux through a surface is a measure of the flow through that surface. Therefore, the divergence at a point is equal to the flux through a small cube surrounding that point divided by the volume of the cube.

What are some real-world applications of flux through each face on a cube?

Flux through each face on a cube is commonly used in physics and engineering to study fluid flow, electric and magnetic fields, and heat transfer. For example, it can be used to analyze the flow of air over an airplane wing, the flow of electricity through a circuit, or the transfer of heat through a building's walls. It is also used in computer graphics and simulations to model fluid and particle movements in virtual environments.

Similar threads

Flux Through a Cube's Face with our Point Charge at a Corner
Replies
6
Views
3K
Flux due to a charge located at the corner of a cube
Replies
6
Views
2K
Elec. flux through the top side of a cube with q at a corner
Replies
4
Views
2K
Flux Through Face of Tetrahedron
Replies
2
Views
2K
Flux linked with lower face of a cube
Replies
2
Views
1K
Electric flux of a cube due to a point charge
Replies
5
Views
6K
Electric Flux through the Face of a Cube
Replies
17
Views
7K
Flux Through a Cube: Calculate Φ & q
Replies
9
Views
6K
Electric flux through one face of the cube.
Replies
4
Views
13K
Calculate flux through face of a cube
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top