Integration limits for Gaussian surface

In summary, the conversation discusses setting up an integral to find the flux through a nonconducting spherical shell with inner radius A and outer radius B. The question is whether the gaussian surface should include B or be just inside it, and whether the limits of integration should go from A to B. It is also mentioned that finding the flux through A or B may be confused with finding the potential difference between them.
  • #1
auk411
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Homework Statement



Say you have a nonconducting spherical shell. A is the inner radius and B is the outer radius. If you wanted to set up an integral to find the flux, would the gaussian surface include B, or be just inside it? That is, would the limits of integration go from A to B?

If the limits did not include the actual surface with the radius B, would you just do something like this: come up with some other variable r_g, where A < r_g < B for the upper limit of integration?
 
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  • #2
auk411 said:
Say you have a nonconducting spherical shell. A is the inner radius and B is the outer radius. If you wanted to set up an integral to find the flux, ...
To find the flux through which surface, A or B? I suspect that you are confusing finding the flux through either A or B with finding the potential difference between A and B.
 

FAQ: Integration limits for Gaussian surface

1. What is a Gaussian surface?

A Gaussian surface is an imaginary surface used in Gauss's Law to simplify the calculation of electric fields. It is a closed surface that completely encloses a charge or charges, allowing for the integration of electric field over the entire surface rather than just a specific point.

2. Why are integration limits necessary for Gaussian surfaces?

Integration limits are necessary for Gaussian surfaces because they define the boundaries of the surface over which the electric field is being integrated. Without integration limits, the calculation of the electric field would be incomplete and inaccurate.

3. How do you determine the integration limits for a Gaussian surface?

The integration limits for a Gaussian surface are determined by the shape and size of the surface, as well as the location and distribution of the charges enclosed within the surface. The limits should be chosen such that the entire surface is enclosed and the calculation of the electric field is simplified.

4. Can the integration limits for a Gaussian surface change?

Yes, the integration limits for a Gaussian surface can change depending on the problem being solved. They may vary depending on the shape and location of the charges, and can also change if the Gaussian surface is moved or resized. It is important to carefully consider and adjust the integration limits for accuracy in the calculation of the electric field.

5. Are there any limitations to using Gaussian surfaces for integration?

While Gaussian surfaces are a useful tool for simplifying the calculation of electric fields, they do have limitations. They can only be used for calculating electric fields in situations where the electric field is constant and symmetric, and they cannot be used for non-electrostatic situations. Additionally, the choice of integration limits can affect the accuracy of the calculation.

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