Ampere's law at work in code

You will write three functions for the fields and forces of long conductors. All of them follow from Ampere's circuital law.

The idea. Inside a round wire of radius $a$ with an even current, $B = \dfrac{\mu_0 I r}{2\pi a^2}$. Outside it, $B = \dfrac{\mu_0 I}{2\pi r}$. Inside a long solenoid, $B = \mu_0 n I$. Two long parallel wires pull on each other with $\dfrac{F}{L} = \dfrac{\mu_0 I_1 I_2}{2\pi d}$ on each metre. Use SI units.

Your tasks.

1. In thick_wire_field, return the field at a distance r from the axis of a round wire of radius a. Use one formula for r < a and another for r >= a.
2. In solenoid_field, return the field inside a long solenoid with n turns in each metre.
3. In force_per_metre, return the force on each metre of one wire. Let a positive result mean an attraction and a negative result a repulsion. A negative current means the opposite direction.