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Find the charged enclosed by a sphere of charge density ρ and radius a.(a) ρ (4πa^2)(b) ρ(4πa^3/3)(c) ρ(2πa^2)(d) ρ(2πa^3/3)I had been asked this question in a job interview.I would like to ask this question from Volume Integral topic in chapter Vector Calculus of Electromagnetic Theory

Answer»

The correct option is (b) ρ(4πa^3/3)

To explain: The CHARGE enclosed by the sphere is Q = ∫∫∫ ρ dv.

Where, dv = R^2 sin θ dr dθ dφ and on INTEGRATING with r = 0->a, φ = 0->2π and θ = 0->π, we get Q = ρ(4πa^3/3).



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