Let there be a spherical symmetric charge distribution with charge density varying as p r = p 0 r R upto r = R and ρ r = 0 for r R , where r is the distance from the origin. The electric field at on a distance r r

Question

Let there be a spherical symmetric charge distribution with charge density varying as p r = p 0 r R upto r = R and ρ r = 0 for r > R , where r is the distance from the origin. The electric field at on a distance r r < R from the origin is given by -

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Correct answer: A. ρ 0 r 2 4 ε 0 R

∮ E → ‍ . d s → = q i n ε 0 ....(1) q i n = ∫ 0 r ρ 4 π r 2 d r = ∫ 0 r ρ 0 r R 4 π r 2 d r = 4 π ρ 0 R r 4 4 = π ρ 0 r 4 R , from (1) E . 4 π r 2 = π ρ 0 r 4 ε 0 R ∴ E = ρ 0 r 2 4 ε 0 R

Let there be a spherical symmetric charge distribution with charge density varying as p r = p 0 r R upto r = R and ρ r = 0 for r > R , where r is the distance from the origin. The electric field at on a distance r r < R from the origin is given by -

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