Solving for Charge Position from Flux and Gaussian Surface

In summary, the conversation discusses the concept of flux and its different definitions. The person was confused about how to find the location of a charge using flux but realized that the two equations given have different applications. The second equation is a more general definition that works in all scenarios while the first one only applies to flat surfaces perpendicular to the field. The value r in Gauss' law represents the radius of a spherical Gaussian surface, not the distance to the charge.
  • #1
Alem2000
117
0
I was a bit confused by a homwork problem that I was working on. The problem is that I found the flux of a charge and I know the demsions of the Gaussian surface it is encolsed in. It doesn't seem right intuitively to be able to find the location of the charge from this information...but mathmatically I am thinking I can solve for r.
[tex]\Phi=\oint _\mathcal{S} \mathbf{E}\cdot d\mathbf{a} = \frac{q_{enc}}{\epsilon _0}[/tex]
and since electric field is the flux over the area i can find it by
[tex]E=\Phi/A[/tex]
so shouldn't I be able to find the position fo the charge from
[tex]\Phi/A=q/4\pi r^2 \epsilon_0[/tex]
this is really confusing, do I have the theory wrong?
 
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  • #2
Yes, you have two different definitions for flux:

[tex] \Phi = E A [/tex]

and

[tex]\Phi=\oint \vec{E}\cdot \vec{da} [/tex]

Notice how the second definition is a generalization of the first one. The first equation only applies to flat surfaces which are perpendicular to the field, the second definition works in general.

Also, the r that you pulled out of Gauss' law is the radius of a spherical Gaussian surface (an hence the place you are looking at the field) , not "the distance to the charge".
 
  • #3
THANK YOU, that makes a lot more sense now!
 

1. How do you solve for charge position from flux and Gaussian surface?

To solve for charge position from flux and Gaussian surface, you can use Gauss's Law, which states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space. By setting up and solving the appropriate equations, you can determine the charge position.

2. What is the relationship between flux and the Gaussian surface?

The Gaussian surface is a hypothetical surface used to calculate electric flux. It is chosen to simplify the calculation and is usually a symmetrical shape, such as a sphere or cylinder. The flux through the Gaussian surface is equal to the flux through the actual surface, making it a useful tool for solving for charge position.

3. Can you use any shape for the Gaussian surface?

No, the Gaussian surface must be a symmetrical shape in order for the calculations to work. This is because the electric field and flux are constant over a symmetrical surface, making the equations easier to solve.

4. How does the amount of flux through the Gaussian surface relate to the charge position?

The amount of flux through the Gaussian surface is directly proportional to the enclosed charge. This means that if the enclosed charge increases, the flux will also increase, and vice versa. By measuring the flux through the Gaussian surface, you can determine the charge position.

5. What are the units of flux and how do they relate to charge position?

The SI unit of flux is the volt-meter (V-m) or the newton-meter squared per coulomb (N-m²/C). The flux through the Gaussian surface is a measure of the electric field passing through that surface, and this electric field can be used to determine the charge position. Therefore, the units of flux and charge position are related through the electric field and the permittivity of free space.

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