Question Bank • QB_EXP_EM_GEN_001 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus: Sequences, Infinite Series & Convergence

Subtopic: Ratio test

Question Statement:

For the differential operator $\nabla$, the divergence of the curl of any twice continuously differentiable vector field $\vec{V}$ is always equal to:

Options:

  • (A) 0
  • (B) 1
  • (C) \nabla^2 \vec{V}
  • (D) 3 \vec{V}

Answer Key:

A

Step-by-Step Solution & Explanation

By the fundamental vector identity, $\nabla \cdot (\nabla \times \vec{V}) = 0$ identically for any smooth vector field $\vec{V}$. This represents the physical fact that a vortex line cannot end within the fluid.
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