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