Question Bank • QB_EM_VC_012 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Stokes, Gauss and Green's theorems

Question Statement:

Gauss's Divergence Theorem transforms:

Options:

  • (A) A line integral around a closed curve into a surface integral
  • (B) A surface integral over a closed surface into a volume integral
  • (C) A line integral into a volume integral
  • (D) A volume integral into a line integral

Answer Key:

B

Step-by-Step Solution & Explanation

Gauss's Divergence Theorem states: $\iint_S \vec{F} \cdot \hat{n} \, dS = \iiint_V (\nabla \cdot \vec{F}) \, dV$ It relates the outward flux of a vector field through a closed boundary surface $S$ to the volume integral of its divergence over the enclosed region $V$.
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