Short answers, pulled from the story.
Inductance is the property of an electrical conductor to resist any shift in the electric current flowing through it. This resistance creates a magnetic field around the wire whenever electricity moves inside.
Michael Faraday published his first description of electromagnetic induction in 1831. He wrapped two separate wires around opposite sides of an iron ring for his experiment.
Longer wires have more inductance than shorter ones while thicker wires have less inductance than thinner ones. A single conductor of lamp cord ten meters long made of 18 AWG wire has an inductance of about 20 nanohenries if stretched straight.
Ferromagnetic materials near the conductor complicate these equations because saturation occurs when the core reaches a limit. Inductance changes with current once saturation begins requiring the integral equation instead of simple constants.
The coupling coefficient measures the ratio of actual voltage to theoretical maximum voltage in mutual inductance scenarios. Most authors define this range between zero and one where negative values capture phase inversions of coil connections.