Halliday, Resnick & Walker — Induction and Inductance: Problem 70

70 Figure 30-53 shows two circular regions \(R_1\) and \(R_2\) with radii \(r_1 = 20.0 \text{ cm}\) and \(r_2 = 30.0 \text{ cm}\). In \(R_1\) there is a uniform magnetic field of magnitude \(B_1 = 60.0 \text{ mT}\) directed into the page, and in \(R_2\) there is a uniform magnetic field of magnitude \(B_2 = 75.0 \text{ mT}\) directed out of the page (ignore fringing). Both fields are decreasing at the rate of \(8.50 \text{ mT/s}\). Calculate \(\oint \vec{E} \cdot d\vec{s}\) for (a) path 1, (b) path 2, and (c) path 3.