A square loop of edge length $2 \mathrm{~m}$ carrying current of $2 \mathrm{~A}$ is placed with its edges parallel to the $\mathrm{x}-\mathrm{y}$ axis. A magnetic field is passing through the $x-y$ plane and expressed as $\vec{B}=B_0(1+4 x) \hat{k}$, where $\mathrm{B}_0=5 \mathrm{~T}$. The net magnetic force experienced by the loop is. . . . . . . $\mathrm{N}$.
JEE MAIN 2024, Diffcult
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$\mathrm{B}(\mathrm{x}=0)=\mathrm{B}_0, \quad \mathrm{~B}(\mathrm{x}=2)=9 \mathrm{~B}_0$
$\text { Also, } \mathrm{F}=\mathrm{i} \ell \mathrm{B}$
$\Rightarrow \mathrm{F}_1=\mathrm{i} \ell \mathrm{B}_0 \& \mathrm{~F}_2=9 \mathrm{i} \ell \mathrm{B}_0$
$\mathrm{~F}=\mathrm{F}_2-\mathrm{F}_1=8 \mathrm{i} \ell \mathrm{B}_0=8 \times 2 \times 2 \times 5$
$\mathrm{~F}=160 \mathrm{~N}$
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