a) Find \(\mathcal{E}(R, t)\), the electromotive force (EMF) around a loop that is at distance \(R\) from the \(z\) axis, where \(R\) is restricted to the region outside the iron rod as shown. Take the direction shown in the figure as positive.
Express \(\mathcal{E}(R, t)\) in terms of \(A ,B_{0}, B_{1}, R,{\text {,and any needed constants such as }} \epsilon_{0}, \pi\), and \(\mu_{0}\)
b)
Due to the cylindrical symmetry of this problem, the induced electric field \(\vec{E}(R, t)\) can depend...