Question

Two parallel wires each of length $5m$ are placed at a distance of $10cm$ apart in air. They carry equal currents along the same direction and experience a mutually attractive force of $3.6\times {10}^{-4}N$. Find the current through the conductors.

Answer 1

The force between the current carrying conductors is given by:

$F=\frac{{\mu }_0{I}_1{I}_{2}l}{2\pi a}$

Now, $\because I_1=I_2$,
$I^2=\frac{F\times 2\pi a}{{\mu }_{0}l}$
$=\frac{3.6\times {10}^{-4}\times 2\pi \times 10\times {10}^{-2}}{4\pi \times {10}^{-7}\times 5}$
$I^2=36$
$\therefore I=6A$