Allied & ICAR Exam Bank • ALLIED_2691 NAT • 2 Marks

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Stokes, Gauss and Green's theorems

Question Statement:

Using the divergence theorem, the outward flux of $\vec{F} = 2x\hat{i} + 3y\hat{j} + z\hat{k}$ through the surface of a unit cube $[0,1] \times [0,1] \times [0,1]$ is:

Answer Key:

6

Step-by-Step Solution & Explanation

$\nabla \cdot \vec{F} = 2 + 3 + 1 = 6$. The volume of the unit cube is $V = 1$. Flux = $\iiint_V 6 dV = 6 \times 1 = 6$.
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