Halliday, Resnick & Walker — Magnetic Fields Due to Currents: Problem 48

48 A current is set up in a wire loop consisting of a semicircle of radius 4.50 cm, a smaller concentric semicircle, and two radial straight lengths, all in the same plane. Figure 29-53a shows the arrangement but is not drawn to scale. The magnitude of the magnetic field produced at the center of curvature is \( 47.25 \mu\text{T} \). The smaller semicircle is then flipped over (rotated) until the loop is again entirely in the same plane (Fig. 29-53b). The magnetic field produced at the (same) center of curvature now has magnitude \( 15.75 \mu\text{T} \), and its direction is reversed from the initial magnetic field. What is the radius of the smaller semicircle?