A conducting wire bent in the form of a parabola $y^2 = 2x$ carries a current $i = 2 A$ as shown in figure. This wire is placed in a uniform magnetic field $\vec B = - 4\,\hat k$ $Tesla$. The magnetic force on the wire is (in newton)
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Magnetic force is given by
$\mathrm{dFm}=\mathrm{i} \int \mathrm{d} \vec{\ell} \times \overrightarrow{\mathrm{B}}=\mathrm{i} \int \mathrm{d} \ell(-\hat{\mathrm{j}}) \times(-4 \hat{\mathrm{k}})=4 \mathrm{i} \int \mathrm{d} \ell \hat{\mathrm{i}}$
since $\ell$ and $B$ are perpendicular so
$\mathrm{df}_{\mathrm{m}}=8 \int \mathrm{d} \ell \hat{\mathrm{i}}=8 \times 4 \hat{\mathrm{i}}=32 \hat{\mathrm{i}}$
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