Problem 3.330

Determine the mutual inductance of a doughnut coil and an infinite straight wire passing along its axis. The coil has a rectangular cross-section, its inside radius is equal to $a$ and the outside one, to $b$. The length of the doughnut's cross-sectional side parallel to the wire is equal to h. The coil has $N$ turns. The system is located in a uniform magnetic with permeability $\mu$.