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GATE EC 2015 Set 3 — Question 39

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NAT+2 / -0MediumLine, Surface & Volume IntegralsVector CalculusEngineering MathematicsGauss, Stokes & Green's Theorems

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

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Question

A vector field D=2ρ2aρ+zaz\mathbf{D} = 2\rho^2 \mathbf{a}_\rho + z \mathbf{a}_z exists inside a cylindrical region enclosed by the surfaces ρ=1,z=0\rho = 1, z = 0 and z=5z = 5. Let SS be the surface bounding this cylindrical region. The surface integral of this field on SS (∮SD⋅ds\oint_S \mathbf{D} \cdot d\mathbf{s}) is ______.
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