Q.Two long parallel wires $15\ \text{cm}$ apart carry currents of $10\ \text{A}$ and $15\ \text{A}$ in opposite directions. Find the force per unit length between them, and state whether the wires attract or repel each other.

Two long, straight, parallel wires, separated by distance d and carrying currents $I_1$ and $I_2$, exert a magnetic force on each other: the field of wire 1, at the location of wire 2, is $B=\mu_0I_1/(2\pi d)$ (from the long-straight-wire Biot-Savart result), and wire 2, carrying current $I_2$ in this field, experiences a force per unit length of $F/L=\mu_0I_1I_2/(2\pi d)$. This force is ATTRACTIVE when the two currents flow in the SAME direction (parallel currents) and REPULSIVE when they flow in OPPOSITE directions (antiparallel currents) -- the precise, quantitative version of the simple two-wire demonstration that opens the chapter. …