In high-school level books (for example the german standard text: "Dorn-Bader") I have often seen an explanation of the Lorentz force as on the following picture:
The textbooks consider the superposition of the circular field of the wire and the homogenous field of the magnet (sure the homogenity doesn't matter here). Then the net field as you can see on the picture above on the right is larger on one side of the wire (here on the right) and smalle on the other one. So far so good.
However why does this explain the occurence and direction of the Lorentz force. Do do so, one would need another principle for example that the wire always wants to go to the weaker field regions or something like this. And this principle should be somehow more evident than the Lorentz-force itself (which you can "see" experimentally).
But how is this needed principle exacly forumlated? Why it is correct? Is there any good reason that it is more evident than just taking the Lorentz-force as an experimental fact?
Would be great if someone could clarify the logic of this, evaluate the soundness of the argument and embedd it conceptually and mathematically in the big picture of electromagnetic theory.
Additionally I want to know if the above cited "explanation" has any common name and if there are university level textbooks which proceed in a similar way. I feel that this argument goes back to Michael Faraday (just by the style of reasoning) - so if someone has a reference to the orgin of the argument I would be interested in it, too.
By the way: The magnetic field in the above cited book ("Dorn Bader") is introduced by the interaction of permament magnets...