Halliday, Resnick & Walker — Magnetic Fields Due to Currents: Problem 40

40 The current-carrying wire loop in Fig. 29-47a lies all in one plane and consists of a semicircle of radius 25.0 cm, a smaller semicircle with the same center, and two radial lengths. The smaller semicircle is rotated out of that plane by angle \(\theta\), until it is perpendicular to the plane (Fig. 29-47b). Figure 29-47c gives the magnitude \(B\) of the net magnetic field at the center of curvature versus angle \(\theta\). The vertical scale is set by \(B_a = 10.0\ \mu\text{T}\) and \(B_b = 12.0\ \mu\text{T}\). What is the radius of the smaller semicircle?