Magnets and the Earth's field in code

You will write four functions about a short bar magnet and the field of the Earth.

The idea. A short magnet of moment $m$ has $B = \dfrac{\mu_0}{4\pi}\dfrac{2m}{r^3}$ on its axis. The Earth's field has a horizontal part $B_E\cos\delta$ and a vertical part $B_E\sin\delta$, with the dip $\delta$. A magnet swinging a little has the period $T = 2\pi\sqrt{J/(mB)}$. Use SI units and angles in degrees.

Your tasks.

1. In axial_field, return the field in tesla on the axis of a short magnet of moment m (A m²), at a distance r (m) from its centre. Use k = 1e-7.
2. In horizontal_part, return the horizontal part of the field, for a total field total and a dip dip in degrees.
3. In dip_angle, return the dip in degrees from the horizontal part and the vertical part. Use math.atan2 and math.degrees.
4. In period, return the period in s of a magnet with moment of inertia J, magnetic moment m and field B.