College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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use gauss's law 

Will the electric field of a cylinder that is charged non-uniformly, namely with a charge density p = Po • r² , behave
differently with distance than a uniformly charged cylinder?
1. What about inside?
2. What about outside?
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Transcribed Image Text:Will the electric field of a cylinder that is charged non-uniformly, namely with a charge density p = Po • r² , behave differently with distance than a uniformly charged cylinder? 1. What about inside? 2. What about outside?
Expert Solution
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Step 1

Electric field due to non-uniformly charged cylinder

Given that,

charge density ρ=ρ0.r2

1.

Consider a point p inside the cylinder with radius vector r. To calculate E at P, we take the Gaussian surface to be a shell of radius rg

The non-uniform of height h and radius r.

The area enclosed by the cylinder is

A=2πrh

Charge enclosed by the surface is

 Qen=ρ.VIf dr is the thickness of the shell and h is the height then,Substituting the given values in the equation we getdQen=ρ0r2.2πhr.drQen=0rgρ02πhr3.dr=ρ02πhr44=πr402

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