Question

In a region, the electric field is given by $\vec{E} = (3\hat{i} + 5\hat{j} + 7\hat{k})\ \text{N/C}$. The electric flux through a surface of area $3\ \text{m}^2$ in the $yz$-plane is (in SI units):

• A. 21
• B. 15
• C. 12
• D. 9

Hint:

Electric flux is the dot product of the electric field vector and the area vector. Only the component of the field parallel to the area vector contributes.

Answer 1

The Correct Option is D

Step 1: Understand the orientation of the area vector Since the surface lies in the $yz$-plane, the area vector is along the $x$-axis, i.e., $\vec{A} = A \hat{i} = 3 \hat{i}$. 
Step 2: Use the electric flux formula Electric flux $\Phi_E = \vec{E} \cdot \vec{A}$ \[ \vec{E} = 3\hat{i} + 5\hat{j} + 7\hat{k}, \vec{A} = 3\hat{i} \] \[ \Phi_E = (3\hat{i} + 5\hat{j} + 7\hat{k}) \cdot 3\hat{i} = 3 \times 3 = 9 \]