If you make a single loop of wire bent into a circle and pass a regulated 1 amp current through it you will make a "magnetic field". According to Gauss you have to imagine it is there and calculate accordingly. Then comes an extraordinary performance of human intellect beginning with the magnetic shells construction that shows that the field is uniform across the plane of the loop.
According to Carl Popper we should now measure it to see.
Using a compass as a tangent galvanometer with the earth's field as a reference you can measure the relative strength of the field in the region of the magnet by measuring its deflection (according to the field theory). I have done this and the field is about three times higher near the wire than at the centre. This disproves the magnetic shell construction.
Another basic algorithm is the idea that a series of loops is like one loop multiplied. Well if you do the same thing for six turns then the compass measurement is the same near the wire than at the centre.
This shows that the basic algorithm of what is true on one is true of many as one times the number of repetitions, is false.
I would like to propose a different model: that the magnet is responding to spin-spin interactions as a quantum mechanical effect. These are entirely electrostatic in nature.
The magnetic field does not exist it is fictitious.
The model of the magnetic effect of current is in reality the Lorenz contraction of the moving electrons relative to the fixed charges in the wire and the electrostatic force is mediated by virtual photons.
Since the electrons always occupy the same space in the wire even though they are moving it shows that special relativity is an effect like perspective.
The inductive effect is in reality caused by the acceleration of electrons. Now these little charged particles are governed by quantum mechanics and the energy states up the ladder are discontinuous and the electrons jump from one state to the next the two states overlap and during the transition a fluctuation occurs and a photon emission occurs, just like the hydrogen spectrum.
This photon interacts with just one electron in another wire or the same wire and imparts momentum and energy to change the electron from its original state to its new state. This also means that the photon carries momentum both linear and angular and energy.
This is both mutual and self inductance.
Chris