Calculating the net electric flux

In summary, the net electric flux in a single closed surface is only due to the net charge placed in that surface, as proven mathematically using Gauss' theorem and the fact that the divergence of the electric field is zero for any charges outside the surface.
  • #1
anonymousphys
29
0

Homework Statement


When calculating the net electric flux, we use the equation EA=electric flux. If there are multiple charges in different closed surfaces, do we use the net electric field multiplied by the area for each closed surface to solve the electric flux for a single closed object? How does this work mathematically in terms of the proof for electric flux (more specifically the one where we use a sphere to derive the equation for electric flux? (phi=Q/E)). In other words, how do we prove mathematically that the net electric flux in one closed surface is only due to the net charge placed in the closed surface?



Homework Equations


EA=electric flux
phi=(net charge)/(constant)


The Attempt at a Solution



I believe the answer to the first question is yes?

Sorry if many questions were mixed together, I had many questions on my mind.
Thanks for any replies.
 
Physics news on Phys.org
  • #2
anonymousphys said:
How does this work mathematically in terms of the proof for electric flux (more specifically the one where we use a sphere to derive the equation for electric flux? (phi=Q/E)). In other words, how do we prove mathematically that the net electric flux in one closed surface is only due to the net charge placed in the closed surface?

Hi anonymousphys! :smile:

From Gauss' theorem (the divergence theorem), the flux through a closed surface equals the integral (over the interior) of the divergence of the field …

and the divergence will be zero (.E = 0) for the field produced by any charge outside the surface. :wink:
 
  • #3


I can confirm that the answer to your first question is yes. When calculating the net electric flux for a single closed object, we use the equation EA=electric flux, where E is the net electric field and A is the area of the closed surface. This is because the electric flux is defined as the product of the electric field and the area it passes through.

To understand this mathematically, we can use the proof for electric flux using a sphere. In this proof, we consider a sphere of radius r with a charge Q at its center. We then imagine a small area element dA on the surface of the sphere. The electric field at this point is given by E=kQ/r^2, where k is a constant. Thus, the electric flux through this small area element is given by d(phi)=EdA=kQdA/r^2.

Now, to find the net electric flux through the entire surface of the sphere, we need to integrate this expression over the entire surface. This gives us the equation phi=integral of kQdA/r^2, which simplifies to phi=Q/k, where Q is the net charge inside the sphere.

This shows that the net electric flux through a closed surface is only due to the net charge placed inside the surface. This is because the electric field due to any external charges cancel out at every point inside the surface, leaving only the electric field due to the charge inside the surface.

I hope this explanation helps to clarify your understanding of electric flux and its mathematical proof. Let me know if you have any further questions.
 

1. What is net electric flux?

Net electric flux is a measure of the amount of electric field passing through a given area. It is calculated by taking the dot product of the electric field and the area vector.

2. How do you calculate the net electric flux?

The net electric flux can be calculated by taking the integral of the dot product of the electric field and the area vector over a closed surface.

3. What is the significance of calculating net electric flux?

Calculating net electric flux allows us to understand the strength and direction of the electric field passing through a given surface. It is an important concept in understanding the behavior of electric charges and fields.

4. What are the units for net electric flux?

The units for net electric flux are newton-meters squared per coulomb (N*m^2/C), or volts per meter (V/m).

5. How does net electric flux relate to Gauss's law?

Gauss's law states that the net electric flux through a closed surface is equal to the charge enclosed by the surface divided by the permittivity of free space. Calculating net electric flux allows us to apply Gauss's law and determine the electric field in a given region.

Similar threads

  • Introductory Physics Homework Help
Replies
12
Views
962
  • Introductory Physics Homework Help
Replies
2
Views
811
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
630
  • Introductory Physics Homework Help
Replies
2
Views
972
  • Introductory Physics Homework Help
Replies
15
Views
3K
  • Introductory Physics Homework Help
Replies
7
Views
4K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Back
Top