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A solid non-conducting sphere or radius R is uniformly charged with volume charge density of p. Find the electric field inside the sphere. r< R. b. pr / 3ɛ0 c. pR / 3ɛor? d. pr² / 3ɛ,R e. pR? / 3ɛor a. zero

A solid non-conducting sphere or radius R is uniformly charged with volume charge density of p. Find the electric field inside the sphere. r< R. b. pr / 3ɛ0 c. pR / 3ɛor? d. pr² / 3ɛ,R e. pR? / 3ɛor a. zero

College Physics
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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A solid **non-conducting** sphere of radius \( R \) is uniformly charged with a volume charge density of \( \rho \). Find the electric field inside the sphere for \( r < R \). a. zero b. \( \frac{\rho r}{3 \varepsilon_0} \) c. \( \frac{\rho R^3}{3 \varepsilon_0 r^2} \) d. \( \frac{\rho r^2}{3 \varepsilon_0 R} \) e. \( \frac{\rho R^2}{3 \varepsilon_0 r} \) This question tests the understanding of electric fields in uniformly charged non-conducting spheres, often solved using Gauss's Law.
Transcribed Image Text:A solid **non-conducting** sphere of radius \( R \) is uniformly charged with a volume charge density of \( \rho \). Find the electric field inside the sphere for \( r < R \). a. zero b. \( \frac{\rho r}{3 \varepsilon_0} \) c. \( \frac{\rho R^3}{3 \varepsilon_0 r^2} \) d. \( \frac{\rho r^2}{3 \varepsilon_0 R} \) e. \( \frac{\rho R^2}{3 \varepsilon_0 r} \) This question tests the understanding of electric fields in uniformly charged non-conducting spheres, often solved using Gauss's Law.
Expert Solution
Step 1

The net flux over the Gaussian surface,

ϕnet=E4πr2

 

The charge density,

ρ=qV

 

The charge,

qnet=ρV=ρ4πr33

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