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33. Consider a long, cylindrical charge distribution of radius R with a uniform charge density p. Find the electric field at distance rfrom the axis, where r

33. Consider a long, cylindrical charge distribution of radius R with a uniform charge density p. Find the electric field at distance rfrom the axis, where r

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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Figure P24.32 33. Consider a long, radius R with a uniform charge density p. Find the electric field at distance rfrom the axis, where r< R. cylindrical charge distribution of
Transcribed Image Text:Figure P24.32 33. Consider a long, radius R with a uniform charge density p. Find the electric field at distance rfrom the axis, where r< R. cylindrical charge distribution of
Expert Solution
Step 1

Given the charge density of the cylinder is ρ so if Q is the net charge in the cylinder R is the Radius and L is the length of the cylinder then:

Q =ρ(πR2L) ρ =QπR2L                                                                                                                  ...1 

Now by the Gauss law the electric flux is given by:

ϕ = qinε0qin = charge inside the surfaceε0   = electrical permittivity

now let r < R

then the net charge inside the cylinder with radius r will be:

qin=ρ(πr2L)     =Qπr2LπR2Lqin= Qr2R2

 

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