Two long, straight, parallel conducting wires separated by a distance \(d\) carry steady currents of equal magnitude \(I\) in the same direction. In the absence of an external field, wire 1 exerts an attractive magnetic force per unit length \(f_0\) directly on wire 2. A uniform external magnetic field \(\vec{B}_{\text{ext}}\) is subsequently established throughout the entire region, oriented perpendicular to the plane containing the wires. Although the total magnetic force measured on each wire changes, the mutual force per unit length that wire 1 exerts on wire 2 remains equal to \(f_0\). Which of the following provides the correct physical explanation for this observation?