A surface of area \( \vec{A} = 2\hat{\imath} - 3\hat{k} \) exists in a region of electric field \( \vec{E} = a\hat{\imath} + b\hat{\jmath} \). The net flux passing through the surface is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 2a \)
The electric flux through a surface of area vector \( \vec{A} \) in a uniform field is the dot product \( \Phi = \vec{E}\cdot\vec{A} \); only the components that lie along the same axis multiply.
\( \displaystyle \Phi = (a\hat{\imath} + b\hat{\jmath})\cdot(2\hat{\imath} - 3\hat{k}) = a(2) + b(0) + 0(-3) = 2a \)
The field has no \( \hat{k} \) component and the area vector has no \( \hat{\jmath} \) component, so \( b \) does not contribute.