GATE_AE_2027_MOCK_05_Q37
GATE 2027 Aerospace Engineering All-India Master Mock 05 (High-Yield Comprehensive Grand Finale)
MCQ · 2 Marks
Engineering Mathematics • Calculus • Partial Derivatives & Vector Calculus
A vector field F is said to be conservative (irrotational) in a simply connected domain if and only if:
(A) curl(F) =
abla imes F = 0
(B) div(F) =
abla . F = 0
(C) F . F = 1
(D) The magnitude of F is constant everywhere
Answer Key:
A
Step-by-Step Verified Solution
### Solution: A vector field is conservative if and only if its curl is identically zero, which allows F to be expressed as the gradient of a scalar potential \phi: F = abla \phi. Correct: A.