### Application of Gauss' Law to a Uniformly Charged Sphere**Problem Statement:**4. Use Gauss' Law to calculate the electric field a) inside and b) outside of a sphere of radius \( R \) with charge \( Q \) distributed uniformly throughout its volume.**Explanation:**To tackle this problem using Gauss' Law, we need to consider two regions:a) **Inside the Sphere**: We consider a Gaussian surface within the sphere. For a radius \( r \) (where \( r < R \)), the charge enclosed by the Gaussian surface is proportional to the volume of the sphere inside radius \( r \).b) **Outside the Sphere**: Here, we consider a Gaussian surface outside the sphere. For a radius \( r \) (where \( r > R \)), the entire charge \( Q \) is enclosed within this Gaussian surface.**Detailed Steps and Concepts:**1. **Gauss' Law**: It states that the electric flux through a closed surface is proportional to the charge enclosed by the surface. Mathematically, \[ \oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\epsilon_0} \] where \( \vec{E} \) is the electric field, \( d\vec{A} \) is the differential area on the closed surface, and \( Q_{\text{enc}} \) is the charge enclosed by the surface.2. **Inside the Sphere**: For a Gaussian surface of radius \( r \), the enclosed charge \( Q_{\text{enc}} \) is: \[ Q_{\text{enc}} = Q \left( \frac{r^3}{R^3} \right) \] Using Gauss' Law: \[ E \cdot 4\pi r^2 = \frac{Q_{\text{enc}}}{\epsilon_0} = \frac{Q \left( \frac{r^3}{R^3} \right)}{\epsilon_0} \] Solving for \( E \): \[ E = \frac{Q r}{4 \pi \epsilon_0 R^3} \]3. **Outside the Sphere**: For a Gaussian surface of radius \( r \), the enclosed

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Answered: 4. Use Gauss' Law to calculate the…

4. Use Gauss' Law to calculate the electric field a) inside and b) outside of a sphere of radius R with charge Q distributed uniformly throughout its volume.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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