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 = \to B . \to A

$ϕ = \vec{B} . \vec{A}$

Step 1: Find the flux.

Here,

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

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

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

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

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