In old textbooks we use to see the law for magnetic force between magnetic poles ( i.e F = k M1xM2/r square, where M1 and M2 are the strength of magnetic poles, and k is the proportionality constant), but in modern textbooks we do not see the above law.
I am not sure about the origin of the magnetic charge in the old text books because based on Maxwell's model in classical electrodynamics, there is no magnetic charge in nature. But the idea of electromagnetic duality has been interesting since Maxwell's formulation. This idea proposes that symmetry of nature implies that Maxwell's equations would be symmetric with respect to electric and magnetic charges. Today high energy physics predicts various classes of solutions including different configuratios of magnetic monopoles.
Whereas, classically, the magnetic charges could take any values, like the electric charges, since Dirac's work in 1931, it is known that, if magnetic monopoles *did* exist, then electric charges would be quantized and the magnetic charges would be related in a very specific way to the electric charges (the Dirac quantization condition). Cf. Milton's review on the experimental constraints:
http://arxiv.org/abs/hep-ex/0602040 ``Theoretical and Experimental Status of Magnetic Monopoles''
The ``magnetic'' monopoles of Grand Unified Theories are totally different from the magnetic monopoles in electrodynamics: the former are *regular* solutions of the (classical) equations of motion, whereas the latter are singular sources that must be *added* by hand (like the electric charges) and whose equations of motion are not the Maxwell equations, cf. S. Coleman, ``Classical lumps and their quantum descendants'' in ``Aspects of symmetry'' and
S.~R.~Coleman, ``The Magnetic Monopole Fifty Years Later,''
In *Les Houches 1981, Proceedings, Gauge Theories In High Energy Physics, Part 1*, 461-552 and Harvard Univ. Cambridge - HUTP-82-A032 (82,REC.OCT.) 97p
available at: http://ccdb5fs.kek.jp/cgi-bin/img_index?8211084
In spite to write the magnetic force between poles in special units (4 pi mu-zero=1) without adverticing it, the question is very interesting and the answers confusing. The magnetic monopole is an electrodynamics topological solution ( non-zero first homotopy term) which has nothing to do with magnetic poles which are associated to small currents or magnetic dipoles. One electron moving in its orbita has an electric current which provides a Bohr magneton.
Going to the question, my anser is that nowadays the magnetostatic problems where they are very useful are solved with software packages and they do not enter really into these complex calculations which didn't present too much physics. In any case let me to give you a good text where these concepts are used for defining magnetic wells or magnetic domains in a simple form.
Soshin Chikazumi, Physics of Ferromagnetism, Oxford University Press, 2005.
Would you present such a formula in your own book, when you know no magnetic point-like monopoles were ever found in Nature?
It is funny indeed: sometimes we still encounter "magnetic (surface) charges" being considered in magnetostatic problems. Yet, those old books usually started with figures showing that after bisection of a bar magnet we obtain two smaller bar magnets, not separate magnetic charges, isn't it?
Dear Marek,
One thing is a magnetic monopole, that is allowed by Physics although it was not found, and another very different are magnetic poles which can help us to make analytical calculations. For instance, the calculation of the demagnetize factor of a sphere or cube are examples of how useful is to assume magnetic poles.
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