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  4. The force per unit length between two straight conductors separated by a distance of 0.02 m is 2 × 10-3 N m-1. The current in one conductor is 10 A and that in the other conductor is

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Q. The force per unit length between two straight conductors separated by a distance of 0.02 m is 2 × 10-3 N m-1. The current in one conductor is 10 A and that in the other conductor is

AIIMSAIIMS 2015Moving Charges and Magnetism

Solution:

Force per unit length between two parallel current carrying wire is given by
$F=\frac{\mu_{0}}{2\pi} \frac{I_{1}I_{2}}{r}$
Here, $\frac{\mu_{0}}{4\pi}=10^{-7}NmA^{-2}, r=0.02 m$
$F=2\times10^{-3}Nm^{-1}, I_{1}=10 A, I_{2}=?$
So ,$\quad2\times10^{-3}=2\times10^{-7}\times\frac{10\times I_{1}}{0.02}$
$\quad\quad0.02\times10^{4}=10 I_{1}=\quad\therefore I_{1}=20 A$