First slide

Force on a current carrying wire placed in a magnetic field

Question

A B C is a current carrying conductor carrying a current i = 2A. If length of the segment Ab is $3 \sqrt{3}$ m, then what should be the length of BC . So that net force on the conductor ABC becomes zero?

Moderate

A

$6 m$
B

$4 m$
C

$5 \sqrt{3} m$
D

$4 \sqrt{3} m$

Solution

$\vec{F} = i \vec{l_{e}} \times \vec{B}$
Where le = Ac = equivalent length. It is evident that $\vec{F}$ is zero when $\vec{l_{e}}$ and $\vec{B}$ are parallel (as shown in the figure).
$∴ BC = AB / \cos 30^{0} = \frac{3 \sqrt{3}}{(\frac{\sqrt{3}}{2})} m = 6 m$

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