Mechanical Force on a Magnet. (77) In any part of the field not traversed by electric currents the distribution of magnetic intensity may be represented by the differential coefficients of a <s>quantity<\s> function which may be called the magnetic potential. When there are no currents in the field this quantity has a single value for each point. When there are currents, the <s>function<\s> potential has a series of values at each point, but its differential coefficients have only one value, namely d[phi]/dx = [alpha] d[phi]/dy=[beta] d[phi]/dz=[gamma] Substituting these values of [alpha] [beta] [gamma] in the expression (Eq<sup>n 38) for the intrinsic energy of the field, and integrating by parts it becomes [capital sigma]{[phi]1/8[pi] (d[mu][alpha]/dx + d[mu][beta]/dy + d[mu][gamma]/dz)}dV <s>Now<\s> The expression [capital sigma](d[mu][alpha]/dx + d[mu][beta]/dy + d[mu][gamma]/dz)}dV = [capital sigma]mdV (39) indicates the number of lines of magnetic force which have their origin within the space V. Now a magnetic pole is known to us only as the origin or termination of lines of magnetic force, and a unit pole is one which has 4[pi] lines belonging to it since it produces unit of magnetic intensity at unit of distance over a sphere whose surface is 4[pi]. Hence if m is the amount of free positive magnetism in unit of volume, the above expression may be written 4[pi]m and the expression for the energy of the field becomes E = [capital sigma]([half][phi]m)dV (40) If there are two magnetic poles m<sub>1 <\sub> and m<sub>2<\sub> producing potentials [phi]<sub>1<\sub> & [phi<sub>2<\sub> in the field, then if m<sub>2<\sub> is moved a distance
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Manuscript details
 Author
 James Clerk Maxwell
 Reference
 PT/72/7
 Series
 PT
 Date
 1864
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Cite as
J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7
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