Two along parallel wires are hung by $4 c m$ long chords from a common axis. The wires have mass $0.0125 K g / m$ and carry equal currents in opposite direction. Find the current in each wire if the cords hang at $6^{0}$ with the vertical as shown in $F i g . (a) -$

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$717 A$

$71.7 A$

$22.3 A$

$11.2 A$

answer is B.

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Detailed Solution

$\frac{d F}{d l} rep = \frac{μ_{0} I^{2}}{2 π (2 d)} = T \sin 6^{°}$

$\frac{m g}{4} = T \cos 6^{°}$ $\tan 6^{°} = \frac{μ_{0} I^{2}}{4 π d m g}$

$I = \sqrt{\frac{\tan 6^{°} (4 π 4 \sin 6^{°}) m g \times 10^{- 2}}{μ_{0}}}$

$= \sqrt{\frac{{(. 1)}^{2} \times 4 π \times 4 \times . 0.125 \times 10 \times 10^{- 2}}{4 π \times 10^{- 7}}} = 22.3 A$

$\tan 6^{°} = \sin 6^{°} = \frac{6 \times π}{180} = . 1$

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