Question

Two long parallel conductors carry currents of 12A and 8A respectively in the same direction. If the wires are 10 cm apart, find where the third parallel wire also carrying a current must be placed so that the force experienced by it shall be zero. Answer in the form of $x\times {10}^{-2}m.$ Find x.

Answer 1

For the force on the third conductor to be zero, the direction of the flux density due to the current flowing in the two wires must be opposite in the position of the wire.
$\therefore$ Third wire must be placed between the wire. Let the third wire placed at a distance x m from the wire carrying 12 A, then $B_1=B_2$

$\frac{{\mu }_o{I}_1}{2\pi x}=\frac{{\mu }_o{I}_2}{2\pi (0.1-x)}$

$\frac{12}{x}=\frac{8}{0.1-x}$

$\frac{3}{x}=\frac{2}{0.1-x}$

$0.3=5x=\frac{0.3}{5}=0.06m$