Electric Field of an Infinitely Long Insulating Cylinder

[sicrayan]

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.

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

 

[tiny-tim]

hi sicrayan!

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[sicrayan]

Hi
Thank you for your answer.
My unsuccessful solution:
lets take the length l,
for r<R,

why?

 

[tiny-tim]

hi sicrayan!

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

it isn't, you need to integrate