Allied & ICAR Exam Bank • ALLIED_0053 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Divergence and curl

Question Statement:

For any twice continuously differentiable scalar field $\phi$, $\nabla \times (\nabla \phi)$ is identically:

Options:

  • (A) $\vec{0}$ (null vector)
  • (B) $\nabla^2 \phi$
  • (C) $\nabla \phi$
  • (D) $1$

Answer Key:

A

Step-by-Step Solution & Explanation

The curl of any gradient field is identically zero: $\text{curl}(\text{grad } \phi) = \vec{0}$.
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