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Compute divergence theorem for D = 5r^2/4 i in spherical coordinates between r = 1 and r = 2 in volume integral.(a) 80 π(b) 5 π(c) 75 π(d) 85 πI had been asked this question in a job interview.The doubt is from Volume Integral topic in section Vector Calculus of Electromagnetic Theory

Answer»

The CORRECT answer is (c) 75 π

The explanation is: D.ds = ∫∫∫ Div (D) dv, where RHS needs to be computed.

The divergence of D given is, Div(D) = 5r and dv = R^2 sin θ dr dθ dφ. On integrating, r = 1->2, φ = 0->2π and θ = 0->π, we get Q = 75 π.



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