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A long isolating cylinder with radius R and a charge density ρ(s) = 3λ πR3 (R...

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Physics

A long isolating cylinder with radius R and a charge density

ρ(s) = 3λ πR3 (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.

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