Help Solving Gauss' Law Homework Problem

[catz]

Homework Statement

Trying to find E field inside a sphere radius a with volume charge density rho = k/r

Homework Equations

Gauss' law

The Attempt at a Solution

I set up a spherical shell radius R (R<a)
I found the charge inside by integrating rho from 0 to R (Q = 2*pi*a*R^2)

put these infos into gauss law, got E = k/(2(epsilon))

It just seems weird that the E field inside is constant even though the volume density is not. I guess it might be because the surface area of the gauss shell increases with R but the density drops off as 1/R.

Also, integrating from the origin seems like it might be a mistake (rho -> inf as r-> 0)

 

[Falcons]

Rho is the volume charge density, correct? Is there something you're missing when you go to find the charge enclosed?

 

[JaredJames]

Just a point of frustration on my part, please name your thread appropriately next time - I believe the rules do specify this.