Orbits in a magnetic field in code

You will write three small functions about a charge in a uniform magnetic field. They use $r = \dfrac{mv}{qB}$ and $T = \dfrac{2\pi m}{qB}$.

The idea. In a field at right angles to its velocity, a charge goes round a circle. If the velocity is at an angle $\theta$ to the field, the path is a helix. All quantities are in SI units. The charge is given as a positive number in coulomb. The angle is in degrees.

Your tasks.

1. In orbit_radius, return the radius of the circle in m, for a velocity at right angles to the field.
2. In orbit_period, return the time for one turn in s.
3. In helix, return the radius and the pitch of the path in m, as a pair (radius, pitch).