Halliday, Resnick & Walker — Magnetic Fields Due to Currents: Problem 46

46 In Fig. 29-51a, wire 1 consists of a circular arc and two radial lengths; it carries current \(i_1 = 0.20 \text{ A}\) in the direction indicated. Wire 2, shown in cross section, is long, straight, and perpendicular to the plane of the figure. Its distance from the center of the arc is equal to the radius \(R\) of the arc, and it carries a current \(i_2\) that can be varied. The two currents set up a net magnetic field \(\vec{B}\) at the center of the arc. Figure 29-51b gives the square of the field’s magnitude \(B^2\) plotted versus the square of the current \(i_2^2\). The vertical scale is set by \(B_s^2 = 10.0 \times 10^{-10} \text{ T}^2\). What angle is subtended by the arc?