### Induction

Two straight coils of the length $l$ have a common yoke with the magnetic constant (permeability) $\mu$. The cross-section of both coils $S$ is the same. Numbers of turns are $N_1$ and $N_2$, respectively. Find the inductance coefficients $L_{11}$, $L_{12}$, $L_{21}$, and $L_{22}$.