Compute the Gauss law for D = 10ρ^3/4 i, in cylindrical coordinates with ρ = 4m, z = 0 and z = 5, hence find charge using volume integral.(a) 6100 π(b) 6200 π(c) 6300 π(d) 6400 πThe question was asked during an online interview.The doubt is from Volume Integral topic in portion Vector Calculus of Electromagnetic Theory

Compute the Gauss law for D = 10ρ^3/4 i, in cylindrical coordinates w

1.	Compute the Gauss law for D = 10ρ^3/4 i, in cylindrical coordinates with ρ = 4m, z = 0 and z = 5, hence find charge using volume integral.(a) 6100 π(b) 6200 π(c) 6300 π(d) 6400 πThe question was asked during an online interview.The doubt is from Volume Integral topic in portion Vector Calculus of Electromagnetic Theory
Answer» The correct choice is (d) 6400 π Easy explanation: Q = D.ds = ∫∫∫ Div (D) DV, where RHS needs to be computed. The divergence of D given is, Div(D) = 10 ρ^2 and dv = ρ dρ dφ dz. On integrating, ρ = 0->4, φ = 0->2π and Z = 0->5, we get Q = 6400 π.

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