Question Bank NAT • 2 Marks Section 1: Mathematical Physics Mathematical Physics - Module 4

QB_PH_021: Mathematical Physics - Module 4

Question Statement

Let $\mathbf{F} = -y\hat{i} + x\hat{j}$. The circulation $\oint_C \mathbf{F} \cdot d\mathbf{r}$ along a circle of radius $R = 3$ centered at origin in $xy$-plane is $k\pi$. The integer $k$ is:
Correct Answer
18, 18
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $\nabla \times \mathbf{F} = 2\hat{k}$. Circulation $= 2 \times \pi(3^2) = 18\pi$.
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