The force between two parallel currents \(I_{1}\) and \(I_{2}\) separated by a distance \(r\), has a magnitude per unit length given by \[\frac{F}{l} = \frac{\mu_{0}I_{1}I_{2}}{2\pi r}.\] The force is...The force between two parallel currents \(I_{1}\) and \(I_{2}\) separated by a distance \(r\), has a magnitude per unit length given by \[\frac{F}{l} = \frac{\mu_{0}I_{1}I_{2}}{2\pi r}.\] The force is attractive if the currents are in the same direction, repulsive if they are in opposite directions.
This field is uniform along wire 2 and perpendicular to it, and so the force \(F_{2}\) it exerts on wire 2 is given by \(F = IlB sin\theta\) with \(sin \theta = 1\): \[F_{2} = I_{2}lB_{1}.\label{22.11...This field is uniform along wire 2 and perpendicular to it, and so the force \(F_{2}\) it exerts on wire 2 is given by \(F = IlB sin\theta\) with \(sin \theta = 1\): \[F_{2} = I_{2}lB_{1}.\label{22.11.2}\] By Newton’s third law, the forces on the wires are equal in magnitude, and so we just write \(F\) for the magnitude of \(F_{2}\). (Note that \(F_{1} = -F_{2}\).) Since the wires are very long, it is convenient to think in terms of \(F/l\), the force per unit length.
