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

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Homework Help Overview

The problem involves determining the electric field using Gauss's law for a system consisting of a charged sphere and a surrounding spherical shell. The charge distribution is specified, and the task is to analyze the electric field in three distinct regions based on the distance from the center of the sphere.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of Gauss's law and the initial steps required to approach the problem. Questions about the Gaussian surface and the relevant charge distributions are raised. Some participants express uncertainty about how to proceed despite having a conceptual understanding of the formula.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the problem. Some have begun to outline their understanding of the Gaussian surface and the total charge enclosed, while others seek clarification on foundational concepts and resources. There is no explicit consensus yet, but guidance is being offered regarding the structure of the problem.

Contextual Notes

Participants mention the absence of a textbook as a constraint and express a need for external resources to aid their understanding. There are indications of varying levels of familiarity with the concepts involved, which may affect the discussion's progression.

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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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
 
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.
 
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?
 

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