What I expected: what you find in literature: like Newton's gravity law : F :: 1/r^2. Or if you prefer to express that different: In a rotatory symmetric system {\nabla\cdot B == 0} everywhere, the same since there is no source or sink of B outside the magnets.
On log-log paper that gives a line with slope 2:1. For all 6 different sets of magnets the points lie an a perfect straight line, but their slope is alike, but far from 1:2.
What I am after is confirmation that more people have measured that, and if so, how they explain it.
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By the way: When you let the distance decrease slowly, the magnets (which one?) do the work F * \delta l. Where does that energy come from? The only thing I can think of is internal energy, which means that they grow colder. Has anybody measured that? Does there exist a book on the thermodynamic theory of magnetism?
One more, probably stupid question:
Suppose I have a copper wire from me to the other end of the table, 5 cm above the table. Current from me to the other end, 15 - 20 Amperes.
I move a compass across the table under the wire. Which way can I expect the pointer marked "N" of my compass will point to? Left or Right?
To make sure that my compass 'feels' the circular field I move it to above the wire. As expected the compasneedle turns to its opposite.
It should be a simple question: What do you expect and why:
a. When below the wire, the pointer marked "N" points to my left, when above to my right
or.
b. below to my right right, when above left?
And I will be very grateful to the one who makes me understand the meaning of "Permeability" of "Nothing".
N