A wire is bent as a parabolic curve and kept in the x-y plane. The curve can be described by the equation x² = 6y. The wire carries a current i = 2A. If a uniform magnetic field $\vec{B} = 2 \times 10^{- 3} \hat{k}$ tesla is applied, force experienced by the wire is nearly:

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$- 1 .5 \hat{j} N$

$2 .5 \hat{j} N$

$- 0 .05 \hat{j} N$

$1 .5 \hat{j} N$

answer is C.

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Detailed Solution

At, y = 6, x = 6

So, effective length of wire is 6+6 = 12 m

$\Rightarrow \vec{l} = 12 \hat{i}$

and $\vec{B} = 2 \times 10^{- 3} \hat{k}$

$\vec{F} = i (\vec{l} \times \vec{B}) = - 0.048 \hat{j} N$

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