Electric Flux/Gauss' Law

In summary, the problem involves finding the electric flux through the top surface of a 2 m x 2 m x 2 m cube with a 10 nC point charge at its center. The electric flux formula is used, taking into account the point charge's electric field and the area of the top surface. The cube is considered closed and uniform, resulting in equal flux passing through each face. The total flux of the cube is calculated, and then divided by 6 to find the flux through the top surface. The final answer is 188.32 N m^2 / C.
  • #1
Go Boom Now
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0

Homework Statement


A 10 nC point charge is at the center of a 2 m x 2 m x 2 m cube. What is the electric flux through the top surface of the cube?

Homework Equations



Electric Flux = E x A x cosθ
Electric Flux = ∫E x dA = Q(inside)/ε
E (point charge) = kq/r^2 where k = 1/(4pi ε)

The Attempt at a Solution


Aside from finding the area, volume, and anything else that might be considered obvious, I've no idea where to head from here. I'm not sure if the cube is completely closed or if the top surface isn't uniform. I'm hoping someone can help walk me through this problem.
 
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  • #2
It's an imaginary cube. So it's closed and doesn't have any properties that could be nonuniform. You can compute the total flux through the cube, right?? Any reason to believe that more passes through one face than any other?
 
  • #3
I'm... not sure? The point charge is in the center of the cube itself, so... no?
 
  • #4
Go Boom Now said:
I'm... not sure? The point charge is in the center of the cube itself, so... no?

Ok, so 1/6 of the total flux must pass through each face. Total flux is easy to compute.
 
  • #5
I think I got it.

Total Flux of Cube = Q (charge) / ε = (10x10^-9) / (8.85x10^-12)

1129.94 / 6 = 188.32 N m^2 / C.

This is the answer I was given. Thanks for the help!
 

1. What is electric flux?

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

2. How is electric flux calculated?

Electric flux is calculated by multiplying the electric field strength by the area of the surface that the field passes through. This can be represented by the equation ΦE = E x A, where E is the electric field and A is the area of the surface.

3. What is Gauss' Law?

Gauss' Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface. It states that the electric flux through a closed surface is equal to the net charge enclosed by that surface divided by the permittivity of free space.

4. How is Gauss' Law used in practical applications?

Gauss' Law is used in a variety of practical applications, such as calculating the electric field of a point charge, analyzing the behavior of electric fields in capacitors, and designing electronic devices. It is also used in the study of electrostatics and magnetostatics.

5. Is electric flux conserved?

Yes, electric flux is conserved. This means that the total electric flux entering a closed surface is equal to the total electric flux leaving that surface. This is a result of Gauss' Law and is a fundamental principle in the study of electromagnetism.

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