Question: Q. 1. A square of side $L$ meters lies in the $x-y$ plane in a region where the magnetic field is given by $\vec{B}=B_{0}(2 \hat{i}+3 \hat{j}+4 \hat{k}) \quad$ Tesla, where $B_{0}$ is constant. The magnitude of flux passing through the square is (a) $2 B_{0} L^{2} \mathrm{~Wb}$. (b) $3 B_{0} L^{2} \mathrm{~Wb}$. (c) $4 B_{0} L^{2} \mathrm{~Wb}$. (d) $\sqrt{29} B_{0} L^{2} W b$
[NCERT Exemplar]
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Solution:
Ans. Correct option : (c)
Explanation: Magnetic flux is defined as the total number of magnetic lines of force passing normally through an area placed in a magnetic field and is equal to the magnetic flux linked with that area.
Square lies in $x-y$ plane in $\vec{B}$ so $\vec{A}=L^{2} \hat{k}$
$Q=B . A$
$=B_{0}(2 \hat{i}+3 \hat{j}+4 \hat{k}) \cdot\left(L^{2} \hat{k}\right)$
$=B_{0}[2 \times \hat{i} \hat{k}+3 \times \hat{j} \hat{k}+4 \times \hat{k} \cdot \hat{k}]$
$=B_{0} L^{2}[0+0+4]$
$=4 B_{0} L^{2} \mathrm{~W}$.
