Question 3.2.7: Determine the force per unit length between two parallel wir...

We use Eq. (3.48) to compute the force. Choose a coordinate system with I_{1}  along the z-axis. This current gives rise to a field B_{1} across I_{2}

Eq. (3.48): dF = I dl × B_{ext}.

B_{1} = – \frac{μ_{o}I_{1}}{2πd}\hat{x}.

The force is given by

F = I_{2} \hat{z} × B_{1}

= – \frac{μ_{o}I_{1}I_{2}}{2πd}\hat{y}            (3.53)

Notice that the force is attractive, it pulls the wires together. If the currents are in opposite directions the wires repel one another.