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

QB_PH_011: Mathematical Physics - Module 4

Question Statement

Evaluate $\iint_S \mathbf{F} \cdot d\mathbf{S}$, where $\mathbf{F} = x\hat{i} + y\hat{j} + z\hat{k}$ and $S$ is a sphere of radius $R = 2$. The value divided by $\pi$ is:
Correct Answer
31.9, 32.1
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $\nabla \cdot \mathbf{F} = 3$. Integral $= 3 \times \frac{4}{3}\pi (2^3) = 32\pi$. Value/$\pi = 32$.
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