Electric Field of an Infinitely Long Insulating Cylinder

AI Thread Summary
The discussion focuses on calculating the electric field of an infinitely long insulating cylinder with a varying volume charge density using Gauss's law. Participants emphasize the importance of integrating the charge density rather than simply multiplying by the area to find the enclosed charge for regions inside and outside the cylinder. The conversation highlights the need for clarity in applying Gauss's law correctly, particularly in determining the electric field for radial distances both less than and greater than the cylinder's radius. Users are encouraged to share their attempts and specific challenges to receive targeted assistance. Accurate integration is crucial for deriving the correct electric field values.
sicrayan
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Homework Statement


An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as given by the following expression where ρ0, a, and b are positive constants and r is the distance from the axis of the cylinder.
symimage.cgi?expr=rho%3Drho_0%28a-r%2Fb%29.gif

Use Gauss's law to determine the magnitude of the electric field at the following radial distances. (Use the following as necessary: ε0, ρ0, a, b, r, and R.)
(a) r < R
(b) r > R

Homework Equations


gauss's law
 

Attachments

  • symimage.cgi?expr=rho%3Drho_0%28a-r%2Fb%29.gif
    symimage.cgi?expr=rho%3Drho_0%28a-r%2Fb%29.gif
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hi sicrayan! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
Hi
Thank you for your answer.
My unsuccessful solution:
lets take the length l,
for r<R,
WEyjR.png

why?
 
Last edited:
hi sicrayan! :smile:

no, you're taking the mass inside radius r as πr2 times ρ(r) …

it isn't, you need to integrate :wink:
 
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