Ncert Exercises & Solutions

A square of side \(L\) meters lies in the \(XY\text-\)plane in a region where the magnetic field is given by \(\vec{B}=B_{0}\left ( 2\hat{i} +3\hat{j}+4\hat{k}\right )\text{T}\) where \(B_{0}\) is constant. The magnitude of flux passing through the square will be:
1. \(2 B_{0} L^{2}~\text{Wb}\)
2. \(3 B_{0} L^{2}~\text{Wb}\)
3. \(4 B_{0} L^{2}~\text{Wb}\)
4. \(\sqrt{29} B_{0} L^{2}~\text{Wb}\)

ϕ = \vec{B} . \vec{A}

Step 1: Find the flux.

Here,

\vec{A} = L^{2} \hat{k} and \vec{B} = B_{0} (2 \hat{i} + 3 \hat{j} + \hat{k}) T

ϕ = \vec{B} . \vec{A} = B_{0} (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) . L^{2} \hat{k} = 4 B_{0} L^{2} Wb

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