Question

An electric field is given by \( \vec{E} = (6\hat{i} + 5\hat{j} + 3\hat{k}) \, \text{N/C \). The electric flux through a surface area \( 30\hat{i} \, \text{m}^2 \) lying in the YZ-plane (in SI units) is:}

• A. \( 180 \)
• B. \( 90 \)
• C. \( 150 \)
• D. \( 60 \)

Hint:

When calculating electric flux, only the components of the electric field vector that align with the area vector contribute to the dot product.

Answer 1

The Correct Option is A

The electric flux \( \Phi \) is given by the dot product of the electric field vector \( \vec{E} \) and the area vector \( \vec{A} \): \[ \Phi = \vec{E} \cdot \vec{A}. \] Given that the area vector is \( \vec{A} = 30\hat{i} \, \text{m}^2 \), and the electric field is \( \vec{E} = 6\hat{i} + 5\hat{j} + 3\hat{k} \), the flux is: \[ \Phi = (6\hat{i} + 5\hat{j} + 3\hat{k}) \cdot (30\hat{i}). \] Only the components along the \( \hat{i} \) direction contribute to the dot product: \[ \Phi = 6 \cdot 30 = 180 \, \text{V·m}. \] Final Answer: \[ \boxed{180 \, \text{V·m}}. \]