Flux, emf and charge in code

You will write three small functions about a coil in a changing field. They use $\Phi = BA\cos\theta$, Faraday's law and $Q = N\Delta\Phi/R$.

The idea. The flux through one turn is $BA\cos\theta$, with $\theta$ the angle between the field and the normal. The emf is the change of flux linkage divided by the time. Areas are in m², fluxes are in Wb.

Your tasks.

1. In flux, return the flux in Wb through one turn. The angle is in degrees.
2. In average_emf, return the size of the average emf in V. The fluxes are through one turn.
3. In charge, return the charge in C that flows round the closed circuit. The size must be positive.