GATE ME 2018 Set 1 — Question 37
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Engineering Mathematics → Vector Calculus → Gauss Divergence Theorem
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Question
The value of the integralover the closed surface bounding a volume , where is the position vector and is the normal to the surface , is
Correct answer
(C) 3V
Solution
By Gauss Divergence Theorem, the surface integral of a vector field over a closed surface is equal to the volume integral of the divergence of over the volume enclosed by :Here, .
Calculate the divergence of :Substitute this into the volume integral:Thus, the value of the integral is .
Calculate the divergence of :Substitute this into the volume integral:Thus, the value of the integral is .
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