GATE 2025 AE – Question 45
$\hat i$ and $\hat j$ denote unit vectors in the $x$ and $y$ directions, respectively. The outward flux of the two-dimensional vector field $\vec v = x\hat i + y\hat j$ over the unit circle centered at the origin is ______ (rounded off to two decimal places).
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Correct answer: 6.25 to 6.31
Explanation
By the divergence theorem the flux equals $\iint\nabla\cdot\vec v\,dA = \iint 2\,dA = 2 \times \pi(1)^2 = 2\pi = 6.28$.