Halliday, Resnick & Walker — Magnetic Fields Due to Currents: Problem 22

22 Figure 29-37a shows, in cross section, three current-carrying wires that are long, straight, and parallel to one another. Wires 1 and 2 are fixed in place on an x axis, with separation \(d\). Wire 1 has a current of \(0.750 \text{ A}\), but the direction of the current is not given. Wire 3, with a current of \(0.250 \text{ A}\) out of the page, can be moved along the x axis to the right of wire 2. As wire 3 is moved, the magnitude of the net magnetic force \(\vec{F}_2\) on wire 2 due to the currents in wires 1 and 3 changes. The x component of that force is \(F_{2x}\) and the value per unit length of wire 2 is \(F_{2x}/L_2\). Figure 29-37b gives \(F_{2x}/L_2\) versus the position \(x\) of wire 3. The plot has an asymptote \(F_{2x}/L_2 = -0.627 \mu\text{N/m}\) as \(x \to \infty\). The horizontal scale is set by \(x_s = 24.0 \text{ cm}\). What are the (a) size and (b) direction (into or out of the page) of the current in wire 2?