Question

A square of side $L$ meters lies in the $x-y$ plane in a region, where the magnetic field is given by
$\vec{B}= B_0 (2\hat{i} + 3\hat{j} +4\hat{k})T$
where $B_0$ is constant. The magnitude of flux passing through the square is

• A. $2B_{0} L^{2}Wb$
• B. $3B_{0} L^{2}Wb$
• C. $4B_{0} L^{2}Wb$
• D. $\sqrt{29}B_{0}L^{2}Wb$

Answer 1

Answer: (C)

Here, $\vec{B} = B_{0} \left(2\hat{i} +3\hat{j} +4\hat{k}\right) T $
Area of the square $= L^2 \hat{k} m^2$
$\therefore $ Flux passing through the square,
$\phi = \vec{B} \cdot \vec{ A} =B_0 (2\hat i + 3\hat j + 4\hat k) \cdot L^2 \hat k $
$= 4\,B_0 L^2 Wb$