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## Homework Statement

A long insulating cylinder has radius R, length l, and a non-uniform charge density per volume [tex]\rho = e^{ar}[/tex] where r is the distance from the axis of the cylinder. Find the electric field from the center of the axis for

i) r < R

ii) r > R

## The Attempt at a Solution

i)

[tex]\oint \vec{E} \cdot d\vec{A} = \frac{\sum Q_{en}}{\epsilon_0}[/tex]

[tex] \vec{E} 2\pi rl = \frac{\sum Q_{en}}{\epsilon_0}[/tex]

So now here is the problem, if it is inside the cylinder I get something like

(1) [tex]\rho V = Q[/tex]

(2) [tex]\rho V' = Q_{en}[/tex]

Divide them out and some algebra and I get

[tex]Q\frac{V'}{V} = Q_{en}[/tex]

Should I keep this? Does it even matter if it was a non-uniform density?

I will stop here before I do ii...