A square of side L meters lies in the xy-plane in a region where the magnetic field is given by \( B = B_0\,(2\mathbf{i} + 4\mathbf{j} + 5\mathbf{k})\,\mathrm{T} \), where \( B_0 \) is constant. The magnitude of flux passing through the square is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 5B_0\,L^{2}\,\mathrm{Wb} \)
The magnetic flux through a flat area is \( \Phi = \vec{B}\cdot\vec{A} \). A square in the xy-plane has its area vector along the z-axis, \( \vec{A} = L^{2}\hat{k} \), so only the \( \hat{k} \) component of the field contributes; the \( \hat{\imath} \) and \( \hat{\jmath} \) components lie in the plane and give no flux.
\( \displaystyle \Phi = B_0(2\hat{\imath} + 4\hat{\jmath} + 5\hat{k})\cdot L^{2}\hat{k} = 5B_0 L^{2}\,\mathrm{Wb} \)