Question #42996

A large stationary circular wire loop of radius $R$ lies in the $xy$-plane, centered at the origin. A small planar coil of area $A$ ($A \ll R^2$) is placed at the origin. The small coil rotates about the $x$-axis with a constant angular velocity $\omega$. At $t=0$, the area vector $\hat{n}$ of the small coil is directed along the $+z$-axis. The small coil carries a time-varying current $I(t) = I_0 t$ (where $I_0$ is a positive constant), such that its magnetic moment is $\vec{m}(t) = I(t) A \hat{n}$. Additionally, a uniform external magnetic field $\vec{B}_{ext} = \beta t \hat{k}$ (where $\beta$ is a positive constant) exists in the entire region. What is the induced electromotive force (EMF) in the large loop at time $t = \frac{\pi}{2\omega}$? Take the counter-clockwise direction in the $xy$-plane (viewed from the $+z$-axis) as positive.