Main Question or Discussion Point
When they teach transformers, they give you the Ampere's law, the Faraday's law, etc. and then derive this well known formula L = μ * N^2 * A / ℓ. And everything is no nice, all these parameters are used to define some other relationships, like the concept of reluctance in magnetic circuits, etc. But it turns out that this formula may only be valid for long single layer solenoids with the coil length >> D. And for multilayer solenoids there are tons of different numeric methods. But I've never seen them discussed in the context of iron core transformers. So how come the well known relationships between Ф, B, A, H, I, E, ℓ etc. captured in various famous laws yield an unusable formula for inductance? For practical purposes, they just give you a universal transformer equation and tell you here is how you calculate the number of turns in the primary to avoid saturation. But what if I want to estimate the actual current in the primary. Then I will need to calculate L. And it turns out to be tricky. In addition to the permeability that varies with current, I am not even sure what formula for L I should use. Imagine you learn for years F=ma and other fundamental stuff that is based on /derived from other stuff and then they tell you meh these only work for some ideal model.