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

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. What is the direction of the electric field?

(b) Use Gauss’ law to derive the magnitude of the electric field as a function of s for s > R.

(c) Use Gauss’ law to derive the magnitude of the electric field as a function of s for s ≤ R.

(d) Compute the electric potential for all s > 0. Sketch the potential as a function of s.

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Solution

genius_generous answered 2 years ago

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