Walker, Halliday & Resnick — Induction and Inductance: Problem 34

Figure 30-35a shows, in cross section, two wires that are straight, parallel, and very long. The ratio \(i_1/i_2\) of the current carried by wire 1 to that carried by wire 2 is 0.25. Wire 1 is fixed in place. Wire 2 can be moved along the positive side of the x axis so as to change the magnetic energy density \(u_B\) set up by the two currents at the origin. Figure 30-35b gives \(u_B\) as a function of the position \(x\) of wire 2. The curve has an asymptote of \(u_B = 1.96 \text{ nJ/m}^3\) as \(x \to \infty\), and the horizontal axis scale is set by \(x_s = 30.0 \text{ cm}\). What is the value of (a) \(i_1\) and (b) \(i_2\)?