A square of side L meters lies in the xy-plane in a region where the magnetic field is given by $B = B_0 (2\hat i + 4\hat j + 5\hat k) T$, 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) → $5B_0\, L^2\, Wb$
$\text{Given: Square of side } L~\text{in the xy-plane}$
$\text{Magnetic field: } \vec{B} = B_0 (2 \hat{i} + 4 \hat{j} + 5 \hat{k})~\text{T}$
$\text{Area vector of the square: } \vec{A} = L^2 \hat{k}$
$\text{Magnetic flux: } \Phi = \vec{B} \cdot \vec{A}$
$\Phi = B_0 (2 \hat{i} + 4 \hat{j} + 5 \hat{k}) \cdot (L^2 \hat{k})$
$\Phi = B_0 \cdot 5 \cdot L^2$
$\Phi = 5 B_0 L^2$
$\text{Answer: } \Phi = 5 B_0 L^2~\text{Wb}$