Halliday, Resnick & Walker — Induction and Inductance: Problem 39

39 A small circular loop of area $2.00 \text{ cm}^2$ is placed in the plane of, and concentric with, a large circular loop of radius $1.00 \text{ m}$. The current in the large loop is changed at a constant rate from $50.0 \text{ A}$ to $-50.0 \text{ A}$ (a change in direction) in a time of $1.00 \text{ s}$, starting at $t = 0$. What is the magnitude of the magnetic field at the center of the small loop due to the current in the large loop at (a) $t = 0$, (b) $t = 0.500 \text{ s}$, and (c) $t = 1.00 \text{ s}$? (d) From $t = 0$ to $t = 1.00 \text{ s}$, is $\vec{B}$ reversed? Because the inner loop is small, assume $\vec{B}$ is uniform over its area. (e) What emf is induced in the small loop at $t = 0.500 \text{ s}$?