Inductors, coupling and energy

You will write three functions that describe coils. They use the results of the last two lessons.

The idea. A long solenoid has $L = \dfrac{\mu_r\mu_0 N^2 A}{l}$. Two coils with coupling $k$ have $M = k\sqrt{L_1L_2}$, and joined in series they have $L = L_1 + L_2 \pm 2M$. The energy stored in an inductor is $\tfrac{1}{2}LI^2$.

Your tasks.

1. In solenoid_inductance, return the inductance in H of a long solenoid. The length and the radius are in m, and mu_r is the relative permeability of the core.
2. In series_inductance, return the inductance in H of two coils joined in series. L1 and L2 are in H, k is the coupling, and aiding is True when the fields point the same way and False when they oppose.
3. In stored_energy, return the energy in J stored by an inductor L in H that carries current in A.