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

## 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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kuruman
Homework Helper
Gold Member
How do you use Gauss's Law? What is the first step? Look in your textbook to get an idea if you have none.

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

kuruman
Homework Helper
Gold Member
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 $$\sigma$$ 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 im not sure how to fill all of the details in and I struggle with deriving some problems.

kuruman
Homework Helper
Gold Member
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?