The electric field in a region is given by $\vec E = (6\hat i + 3\hat j+5\hat k) N/C$. The electric flux due to this electric field through an area $100\, cm^2$ lying in the X-Y plane is:

$5 × 10^{-2}\, Nm^2/C$

The correct answer is Option (4) → $5 × 10^{-2}\, Nm^2/C$

Given: $\vec{E} = 6\hat{i} + 3\hat{j} + 5\hat{k} \ (N/C)$

Area in X–Y plane ⇒ $\vec{A} = A \hat{k}$

A = $100 \ cm^2 = 100 \times 10^{-4} \ m^2 = 10^{-2} \ m^2$

Flux $\Phi = \vec{E} \cdot \vec{A} = (6\hat{i}+3\hat{j}+5\hat{k}) \cdot (10^{-2}\hat{k})$

$\Phi = 5 \times 10^{-2} \ N \, m^2/C$