Confirming Gauss' Law: Finding Flux

In summary, Gauss' Law is a fundamental principle in electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface. It is important because it allows for easy calculation of the electric field at a point. It is expressed as ∮<em>E</em>⋅<em>dA</em> = <em>Q</em><sub>enc</sub>/ε<sub>0</sub> and can be confirmed experimentally. To find the electric flux, the electric field at each point on the surface is calculated and then summed up. Gauss' Law and Coulomb's Law are related, with Coulomb's Law being derived from Gauss' Law.
  • #1
kuahji
394
2
In general I just wanted to see if I was setting this problem up correctly.

We have a cube centered around the origin and a point charge at the origin. The task is to find the flux & confirm Gauss' Law. We are however to complete the integral ourselves. So imagining the top of the cube

q/(4*Pi*[itex]\epsilon)[/itex][itex]\int[/itex][itex]\int[/itex]z/(x^2+y^2+z^2)^(3/2)dxdy

Would this be the correct setup or am I mucking something up?
 
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  • #2
Nevermind, I went through the integral, it came out correctly... though it wasn't pretty.
 

1. What is Gauss' Law and why is it important?

Gauss' Law is a fundamental principle in electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface. It is important because it allows us to calculate the electric field at a point without having to know the exact distribution of charges in space. This makes it a powerful tool for solving many practical problems in electromagnetism.

2. How do you mathematically express Gauss' Law?

Gauss' Law is expressed as ∮E⋅dA = Qenc/ε0, where ∮E⋅dA represents the electric flux through a closed surface, Qenc is the total charge enclosed by that surface, and ε0 is the permittivity of free space.

3. How do you confirm Gauss' Law experimentally?

To confirm Gauss' Law experimentally, we can use a setup with a known charge enclosed by a closed surface and measure the electric flux through that surface. We can then compare the value of the calculated flux using Gauss' Law with the measured value to see if they are equal. If they are equal, then we have confirmed Gauss' Law.

4. What is the process for finding the electric flux through a closed surface?

To find the electric flux through a closed surface, we first need to determine the electric field at each point on the surface. We can then calculate the dot product of the electric field and the differential area vector at each point and sum them up over the entire surface. This will give us the total electric flux through the surface.

5. How does Gauss' Law relate to Coulomb's Law?

Gauss' Law and Coulomb's Law are both fundamental principles in electromagnetism. While Coulomb's Law relates the magnitude of the electric force between two point charges, Gauss' Law relates the electric field at a point to the total charge enclosed by a closed surface. In fact, Coulomb's Law can be derived from Gauss' Law by considering a point charge as a closed surface with zero area.

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