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A conducting wire bent in the form of a parabola $y^{2} = 2 x$ 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 (in newton)

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$- 16 \hat{i}$

$32 \hat{i}$

$- 32 \hat{i}$

$16 \hat{i}$

answer is B.

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Detailed Solution

At $x = 2, y^{2} = 2 x = 2 \times 2$ or $y = 2$

Thus separation, $A B = 4 c m$

The force, $F = B i (A B) = 4 \times 2 \times 4 = 32 N$

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