A nonconducting sphere of radius R carries a volume charge density that is proportional to the distance

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A nonconducting sphere of radius R carries a volume charge density that is proportional to the distance from the center: ρ = Ar for r ≤ R, where A is a constant; ρ = 0 for r > R.

(a) Find the total charge on the sphere by summing the charges on shells of thickness dr and volume 4πr2 dr.

(b) Find the electric field Er both inside and outside the charge distribution, and sketch Er versus r.

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