GATE EE 2025 Set 1 — Question 51
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Engineering Mathematics → Vector Calculus → Gradient, Divergence & Curl
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Question
Let be the unit radial vector in the spherical co-ordinate system. For which of the following value(s) of , the divergence of the radial vector field is independent of ?
Correct answer
(B) -1; (D) 2
Solution
In spherical coordinates, the divergence of a radial vector field is given by . Given , we have . For the divergence to be independent of , the exponent of must be zero: .
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