Rings and dipoles in code

You will write three functions for the field on the axis of a ring and for a dipole in a uniform field.

The idea. A ring has $E = \dfrac{kQz}{(R^2 + z^2)^{3/2}}$ on its axis. A small dipole has $E = \dfrac{2kp}{r^3}$ on its axis. In a uniform field a dipole has the potential energy $U = -pE\cos\theta$.

Your tasks.

1. In ring_field, return the field on the axis of a ring, in N/C. The charge is q_nc in nC, and the radius radius and the distance z are in m.
2. In dipole_axis_field, return the field on the axis of a dipole of moment p (in C m) at a distance r (in m), in N/C. Use the formula for a point far away.
3. In dipole_energy, return the potential energy in J of a dipole of moment p (in C m) in a field field (in N/C), at an angle angle_deg in degrees to the field.