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 purely radial field isHere , soThe divergence is independent of in two distinct ways:
1.The exponent of vanishes: . Then , a constant. This is option (B).
2.The coefficient vanishes: . Then for every , again independent of . This is option (D).
For : , and for : — both depend on , so options (A) and (C) are rejected.Answer: (B) and (D)Continue learning with Success Tracker
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