# Charge density...electric field...electric potential

A (infinitley long) cylindrical non-conducting tube, inner radius a and outer radius b, with charge density p0 sits in a vacuum. Find (show work and derive) and sketch a plot as a function of radius r:

A) the charge density

B) the total charge enclosed in a cylindrical gaussian surface of radius r

C) the electric field

D) the electric potential referenced to the axis (r=0)

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...e.
(B) The total charge enclosed will depend on the radius "r", we have three cases:

(i) r<a: Then charge enclosed is ZERO.
(ii) a<r<b: Charge will be contained between a layer of radius r and the inner layer of radisu "a":
Q = Pi (r^2-a^2) l p0
(iii) r>b: Then charge will be independent of r:
Q = Pi (b^2-a^2) l p0
again note the "l" that is dropped from the problem, but is implicit I guess!
(C) Using the Gauss' law we ...