FIELD RECIPES
B = μ₀nI and F/L = μ₀I²/2πd — the old ampere audited to one ulp.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
Two recipes, no field lines: the field inside a solenoid and the force per meter between parallel wires. This is the wing’s reference card — deliberately modest, two numbers you can hold, audited like everything else on the site.
The solenoid
Inside a long coil the field is mu-nought n I — uniform, axial, blind to the radius. One subtlety stated up front: mu-nought here is the OLD exact value, four pi times ten to the minus seven. Since 2019 it is a measured quantity, shifted five parts in ten to the ten. The module runs on the old one and says so.
The old ampere
Between two parallel wires: mu-nought I-one I-two over two pi d, attracting when the currents run together, repelling when opposed. Set one ampere in each wire, one meter apart, and the force is two times ten to the minus seven newtons per meter — for seventy-one years that sentence WAS the definition of the ampere. The audit finds it one ulp away, because pi cancels algebraically but not bitwise.
One current, both recipes
The sweep drives the shared current from half an amp to six: the solenoid field grows linearly, the wire force quadratically — one knob, two power laws, side by side on the same card.
Audit
Audited: 2.51327 millitesla inside the thousand-turn coil at two amps; eighty micronewtons per meter between the wires — eighty exactly, the dyadics cooperating; the old-ampere prefactor one ulp from two times ten to the minus seven, stated as a float lesson rather than hidden behind a tolerance; and four scaling laws — doubling n, doubling I twice over, doubling d — each audited bitwise.