A wire of arbitrary shape carries a current $I = 2 A$ . Consider the portion of wire between $(0,0, 0)$ and $(4,4, 4) .$ A magnetic filled given by $\vec{B} = (12 \times 10^{- 4} \hat{i} + 2 \times 10^{- 4} \hat{j})$ $T$ exists in the region. The force acting on the given portion the wire is

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The magnetic force in the uniform magnetic field is

$\vec{F} = I (\vec{L} \times \vec{B})$

$\vec{L} = 4 \hat{i} + 4 \hat{j} + 4 \hat{k}$ and

$\vec{B} = (12 \hat{i} + 2 \hat{j}) \times 10^{- 4} T$

$∴ \vec{F} = 8 \times 10^{- 4} [(\hat{i} + \hat{j} + \hat{k}) \times (12 \hat{i} + 2 \hat{j})] N$

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