Halliday, Resnick & Walker — Magnetic Fields Due to Currents: Problem 50

50 Figure 29-55a shows two wires, each carrying a current. Wire 1 consists of a circular arc of radius \(R\) and two radial lengths; it carries current \(i_1 = 1.5 \text{ A}\) in the direction indicated. Wire 2 is long and straight; it carries a current \(i_2\) that can be varied; and it is at distance \(R/2\) from the center of the arc. The net magnetic field due to the two currents is measured at the center of curvature of the arc. Figure 29-55b is a plot of the component of \(\vec{B}\) in the direction perpendicular to the figure as a function of current \(i_2\). The horizontal scale is set by \(i_{2s} = 1.00 \text{ A}\). What is the angle subtended by the arc?