Halliday, Resnick & Walker — Magnetic Fields Due to Currents: Problem 42

42 In Fig. 29-48a, two circular loops, with different currents but the same radius of 2.0 cm, are centered on a y axis. They are initially separated by distance L = 6.0 cm, with loop 2 positioned at the origin of the axis. The currents in the two loops produce a net magnetic field at the origin, with y component \(B_y\). That component is to be measured as loop 2 is gradually moved in the positive direction of the y axis. Figure 29-48b gives \(B_y\) as a function of the position y of loop 2. The curve approaches an asymptote of \(B_y = 7.20 \mu\text{T}\) as \(y \to \infty\). The horizontal scale is set by \(y_s = 10.0 \text{ cm}\). What are (a) current \(i_1\) in loop 1 and (b) current \(i_2\) in loop 2?