Using Gauss's law to determine elctric fields (Calculus based problem)

In summary: The Gaussian surface is a small sphere inside a different sphere. The total electric flux through the small sphere is _____ . The total charge enclosed by the small sphere is _____ .
  • #1
camrylx
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Homework Statement


A sphere of radius R has a total charge +Q, uniformly distributed throughout its volume. It is surrounded by a thick spherical shell of inner radius R and outer radius 2R carrying a total charge -Q, also uniformly distributed throughout its volume. Using Gauss's law, determine the electric field as a function of r, the distance from the center of the sphere for the regions:
1. 0<=r<=R
2. R<=r<=2R
3. r>=2R


Homework Equations


Gauss's Law but from there no idea
 
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  • #2
How do you use Gauss's Law? What is the first step? Look in your textbook to get an idea if you have none.
 
  • #3
Ok like I know the formula I have a good picture draw but not sure how to tackle this problem... And by the way the idea of looking in the textbook to get started would be great if there was a textbook... Feel free to recommend one because I'm on my own with that
 
  • #5
Ok the Gaussian surface would be a small sphere inside a different sphere. I know where +Q and -Q and i know how to find the [tex]\sigma[/tex] and all of that stuff. I know to start with q'=(r^3/R^3)*q and integrate that from 0 to 2pi and i think the 2 radius or something from there. I know coulombs law will come into and will be working this a spherical charge distribution and do some other stuff from there. I've seen a similar problem but I am not sure how to fill all of the details in and I struggle with deriving some problems.
 
  • #6
OK, Let's start with region 1, r < R. Can you describe the Gaussian surface you will need to find the E field? Fill in the blanks:

It is a sphere of radius _____ centered at _____ .

Then can you find the total electric flux through this sphere?

Finally, can you find the total charge enclosed by this sphere?
 

1. What is Gauss's law and how is it used to determine electric fields?

Gauss's law is a fundamental law in electrostatics that relates the electric flux passing through a closed surface to the charge enclosed within that surface. This law can be used to determine the electric field at a point due to a distribution of charges by calculating the flux through a hypothetical surface surrounding the point.

2. Can Gauss's law be used for any type of charge distribution?

Yes, Gauss's law can be applied to any type of charge distribution, whether it is a continuous distribution or a discrete distribution of point charges. The only requirement is that the distribution must be spherically symmetric, cylindrical symmetric, or planar symmetric in order to simplify the calculations.

3. How is calculus used in solving problems involving Gauss's law?

Calculus is used to integrate the electric field over the surface of the closed surface in Gauss's law. This integration involves determining the electric field at each point on the surface and then summing them up using an integral. Calculus is also used to find the charge enclosed within the surface, which is necessary in order to apply Gauss's law.

4. Are there any limitations to using Gauss's law to determine electric fields?

One limitation of using Gauss's law is that it only applies to electrostatics, meaning that the charges must be in a state of equilibrium. Additionally, the charge distribution must have a high degree of symmetry in order for the calculations to be simplified. In more complex situations, such as non-uniform charge distributions, other methods may need to be used.

5. Can Gauss's law be used to determine the electric field at a point outside of a charge distribution?

Yes, Gauss's law can be used to determine the electric field at a point outside of a charge distribution. In this case, the hypothetical surface used in the calculation would enclose the entire charge distribution, and the electric field at the point of interest would be calculated using the total charge enclosed within the surface.

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