Inductance and the Telegrapher's Equations

What is inductance? A circular definition asks us to believe it is the induced magnetic field by a current or a displacement current. But what is it really?

Inductance is the eddy currents experienced when electrons are rushed down a wire as described by Gausses equations described by Maxwell and then Heaviside. The inductance is formed outside a conductor in a dielectric. Eddies within eddies of current rotating around atoms, molecules and groups thereof. This eddy phenomenon that happens around nuclei in a sort of a telegrapher's drift storing energy in angular momentum of electrons and then atomic nuclei themselves. This energy storage ability of a dielectric medium is described by magnetic permeability and electric permeability.

It is interesting to think about how many electrons flow through a wire. One Coulomb is in the order of ten to the eighteen electrons. That is a huge number of charge carriers. The telegrapher's equations point out that some charge bleeds off in the conductance parameter. Mainly the inductance parameter and also the capacitance parameter are important. As the charge heads down the wire certain 'hot carriers' will bleed off into the dielectric and eddy out around a dielectric nucleus. This spin gives the atoms that extra bit of angular momentum which is also known as energy stored in a magnetic field or inductance. It may once have been known as field flux where the field is contained in the dielectric.

Neat to think about how nested these electron eddies can be. More turns in an inductor or electromagnet lead to more feverish eddies or spin. More angular momentum leads to more energy stored in the magnetic field and more inductance.

After a current has been removed from a wire the angular momentum of the electron eddies unwinds. The magnetic field is said to collapse and the spinning electrons have a propensity to collapse into the wire keeping the current going. This is just as the inductor in the telegrapher's equations would have predicted.

There is a reason for those wonky inductance calculations.