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):
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):
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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.
Updated On: Jun 4, 2025
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- 9
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The Correct Option is D
Solution and Explanation
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 $\Phi_E = \vec{E} \cdot \vec{A}$ \[ \vec{E} = 3\hat{i} + 5\hat{j} + 7\hat{k}, \vec{A} = 3\hat{i} \] \[ \Phi_E = (3\hat{i} + 5\hat{j} + 7\hat{k}) \cdot 3\hat{i} = 3 \times 3 = 9 \]
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