Electric Field in an Infinitely Long Cylinder

[skiboka33]

Here's the problem:

An infinately long cylinder of radius R has a volume charge density that varies with the radius as p = p0(a-r/b) where p0, a and b are all positive constants amd r is the distance from the axis of the cylinder. Use Gauss' law to determine the magnitude of the electric field at r<R and r>R.

here's my logic for r < R:

E = k * int[p*dV/r] = k*p0*int[(a-r/b)*dV/r]
-Then sub in V=Pi*r^2*L (solved for r and integrate wrt V)

but what is this L if it's infinite. Also what is the difference being inside or outside of the cylinder? is it just the limits of integration (ie 0-R, or R-r)?

Thanks.

 

[Tide]

Symmetry tells you the electric field is radial and azimuthally symmetric. Gauss' Law relates the flux of electric field through a closed surface and the amount of charge contained therein. Rethink your approach! :)