Question Bank • QB_EM_093 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Divergence and curl

Question Statement:

A vector field $\vec{F}$ is solenoidal if and only if:

Options:

  • (A) $\nabla \times \vec{F} = 0$
  • (B) $\nabla \cdot \vec{F} = 0$
  • (C) $\nabla (\nabla \cdot \vec{F}) = 0$
  • (D) $\nabla^2 \vec{F} = 0$

Answer Key:

B

Step-by-Step Solution & Explanation

A vector field is solenoidal (divergence-free) if $\nabla \cdot \vec{F} = 0$. If $\nabla \times \vec{F} = 0$, the vector field is irrotational (conservative).
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