GATE EE 2017 Set 2 — Question 3
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Engineering Mathematics → Vector Calculus → Gradient, Divergence & Curl
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Question
The figures show diagrammatic representations of vector fields , , and , respectively. Which one of the following choices is true?
Correct answer
(C) · X ≠ 0, × Y ≠ 0, × Z ≠ 0
Solution
1.Field has arrows pointing radially outward from a point, indicating a source. Thus, its divergence is non-zero (). It has no rotational component, so its curl is zero.
2.Field has arrows forming closed circular loops, indicating rotation. Thus, its curl is non-zero (). It has no radial component, so its divergence is zero.
3.Field is a spiral. A spiral has both a radial component (diverging from the center) and a rotational component. Therefore, both its divergence and curl are non-zero ( and ).
Comparing these with the options, choice (C) is the only one that is consistent with these observations.Continue learning with Success Tracker
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