Question

Derive an expression for the force per unit length acting on the two straight parallel current carrying conductors. In which condition will this force be attractive and repulsive? Define the standard unit of current

Answer 1

The magnetic field due to one current carrying wire on the other wire separated by a distance $d$ is given as

$B=\frac{{\mu }_0{I}_1}{2\pi d}$

The force acting on the other wire on a segment of length $l$ is

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

Hence force per unit length of the wire=$\frac{F}{l}=\frac{{\mu }_0{I}_1{I}_2}{2\pi d}$

When the currents in the wire travel in same direction, the force is attractive.

When the wires carry current in opposite direction, the force is repulsive.

The standard unit of current, ampere, is that current which when flowing in two infinite parallel wires one metre apart produces a force between them of $2\times {10}^{-7}N/m$"