A square of side ' L ' metre lies in x-y plane in a region where the magnetic field is B and B = B₀(2i + 3j + 4k), where B₀ is constant. The magnitude of flux passing through the square (in weber) is (a) √(29) B₀ L² (b) 4 B₀ L² (c) 2 B₀ L² (d) 3 B₀ L²

Answer: (b). A square in the x - y plane has area vector A = L² k. φ = B · A = B₀(2i + 3j + 4k) · L² k φ = 4 B₀ L² So the answer is (b) 4B₀L².

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Other: Induction & Displacement Current

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

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Answer: (b)

A square in the $x$ - $y$ plane has area vector $\vec{A} = L^2 \hat{k}$ .
$\phi = \vec{B} \cdot \vec{A} = B_0(2\hat{i} + 3\hat{j} + 4\hat{k}) \cdot L^2 \hat{k}$
$\phi = 4 B_0 L^2$
So the answer is (b) $4B_0L^2$ .

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