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GATE EC 2021 Set 1 — Question 47

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NAT+2 / -0MediumGauss, Stokes & Green's TheoremsVector CalculusEngineering MathematicsLine, Surface & Volume Integrals

Engineering Mathematics → Vector Calculus → Gauss, Stokes & Green's Theorems

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For a vector field D=ρcos⁡2ϕaρ+z2sin⁡2ϕaϕ\mathbf{D} = \rho \cos^2 \phi \mathbf{a}_\rho + z^2 \sin^2 \phi \mathbf{a}_\phi in a cylindrical coordinate system (ρ,ϕ,z)(\rho, \phi, z) with unit vectors aρ,aϕ\mathbf{a}_\rho, \mathbf{a}_\phi and az\mathbf{a}_z, the net flux of D\mathbf{D} leaving the closed surface of the cylinder (ρ=3,0≤z≤2)(\rho = 3, 0 \leq z \leq 2) (rounded off to two decimal places) is __________.
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