Eddy-current losses in code

You will write three small functions about eddy currents. They use the results of the lesson.

The idea. A magnet falling in a metal tube reaches a steady speed where the drag $kv$ equals the weight $mg$. A copper disc in a changing field loses $P = \dfrac{\pi t a^4}{8\rho}\left(\dfrac{dB}{dt}\right)^2$. A thin sheet loses $\dfrac{P}{V} = \dfrac{\pi^2 f^2 B_m^2 d^2}{6\rho}$ in each cubic metre. Use SI units everywhere.

Your tasks.

1. In terminal_speed, return the steady speed in m/s of a magnet of mass mass in kg, when the drag constant is k in kg/s.
2. In disc_heating, return the heat made each second in W in a copper disc. The radius and the thickness are in m, and rate is $dB/dt$ in T/s.
3. In sheet_loss, return the loss in W/m³ in a thin sheet. The thickness d is in m, the frequency f is in Hz, and the peak field b_peak is in T. The resistivity rho is in $\Omega$ m.