The magnetic field existing in a region is given by $\vec B\, = \,{B_0}\,\left( {5 + \frac{x}{l}} \right)\,\hat K$ A square loop of edge $l$ and carrying a current $i$ is placed with its edges parallel to $x-y$ axes. Find the magnitude of the net magnetic force experienced by the loop
Diffcult
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$\overrightarrow{\mathrm{F}}_{\mathrm{SR}}=-\overrightarrow{\mathrm{F}}_{\mathrm{PQ}}$
$\overrightarrow{\mathrm{F}}_{\mathrm{SR}}+\overrightarrow{\mathrm{F}}_{\mathrm{PQ}}=0$
$\overrightarrow{\mathrm{F}}_{\mathrm{SP}}=\mathrm{B}_{0}\left(5+\frac{\mathrm{O}}{\ell}\right) \mathrm{I} \ell=5 \mathrm{B}_{0} \mathrm{I}_{\ell}(-\hat{\mathrm{i}})$
$\overrightarrow{\mathrm{F}}_{\mathrm{QR}}=\mathrm{B}_{0}\left(5+\frac{\ell}{\ell}\right) \mathrm{I} \ell=6 \mathrm{B}_{0} \mathrm{I} \ell(+\hat{1})$
$\overrightarrow{\mathrm{F}}_{\mathrm{net}}=\overrightarrow{\mathrm{F}}_{\mathrm{SP}}+\overrightarrow{\mathrm{F}}_{\mathrm{QR}}=6 \mathrm{B}_{0} \mathrm{I} \ell(\hat{\mathrm{I}})+5 \mathrm{B}_{0} \mathrm{I} \ell(-\hat{\mathrm{I}})=\mathrm{B}_{0} \mathrm{I} \ell(\hat{\mathrm{I}})$
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