Explaining Electric Flux with Enclosed Charges

In summary, the electric flux through a surface is proportional to the charge enclosed within that surface. When the charge is moved towards the edge of the surface, the angle between the area and electric field vectors is no longer always 0 degrees, but the flux remains the same due to the fact that the flux is also dependent on the divergence of the electric field, which is 0 in empty space. Therefore, the flux through the surfaces of both spheres, one with the charge at the center and one with the charge at the edge, must be the same.
  • #1
brushman
113
1
I under stand that electric flux is proportional to the charged enclosed but I don't get why.

Homework Statement


Consider the sphere with the charged enclosed:
[PLAIN]http://electron9.phys.utk.edu/phys136d/modules/m4/images/Image985a.gif

As you can see the area and electric field vectors are always parallel.

Now compare that situation to one exactly the same except the charge is moved towards the edge of the sphere (but still inside).

In the first situation the area and electric field are parallel to each other so will have the max value. In the second situation the angle is not always 0 degrees.

How can situation two have the same electric flux when it has smaller angles?

Homework Equations


flux = E dot A



Thanks
 
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  • #2
hi brushman! :smile:

the flux is ∫∫ E.dA

that is the same as ∫∫∫ ∇.E dxdydz

and ∇.E = 0 in empty space …

so draw a small imaginary sphere with the charge as its centre … the flux through the surfaces of both spheres must be the same (since there's no charge between them) :wink:
 

1. What is Electric Flux?

Electric Flux is a measure of the amount of electric field passing through a given area. It is measured in units of Volts per meter squared (V/m²).

2. How is Electric Flux related to enclosed charges?

Electric Flux is directly proportional to the number of enclosed charges. This means that as the number of enclosed charges increases, the Electric Flux also increases.

3. Can you explain the concept of closed and open surfaces in relation to electric flux?

A closed surface is one that fully encloses a volume, while an open surface does not. Electric Flux is only calculated through closed surfaces, as they fully enclose the charges and allow for accurate measurement.

4. What is the formula for calculating Electric Flux?

The formula for Electric Flux is Φ = E • A • cos(θ), where Φ represents the flux, E is the electric field, A is the area of the surface, and θ is the angle between the electric field and the normal vector of the surface.

5. How is Electric Flux used in practical applications?

Electric Flux is used in various practical applications, such as in electromagnetism and electrical engineering. It is also used in understanding and analyzing the behavior of electric fields and charges in different materials and environments.

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