A long isolating cylinder with radius R and a charge density
Ï(s) = 3λ Ï€R3 (R − s) for s ≤ R , 0   for s > R,
where λ is a fixed positive line charge density (with units C/m)and s denotes the distance from the center of the cylinder.
(a) Explain why the electric field is only a function of s. Whatis the direction of the electric field?
(b) Use Gauss’ law to derive the magnitude of the electric fieldas a function of s for s > R.
(c) Use Gauss’ law to derive the magnitude of the electric fieldas a function of s for s ≤ R.
(d) Compute the electric potential for all s > 0. Sketch thepotential as a function of s.
