tion, for the permanent magnets only, and φ denotes the magnetic potential.[1]
Helmholtz, moreover, applied the principle of energy to systems containing electric currents. For instance, when a magnet is moved in the vicinity of a current, the energy taken from the battery may be equated to the sum of that expended as Joulian heat, and that communicated to the magnet by the electromagnetic force: and this equation shows that the current is not proportional to the electromotive force of the battery, i.e. it reveals the existence of Faraday's magneto-electric induction, As, however, Helmholtz was at the time unacquainted with the conception of the electrokinetic energy stored in connexion with a current, his equations were for the most part defective. But in the case of the mutual action of a current and a permanent magnet, he obtained the correct result that the time-integral of the induced electromotive force in the circuit is equal to the increase which takes place in the potential of the magnet towards a current of a certain strength in the circuit.
The correct theory of the energy of magnetic and electromagnetic fields is due mainly to W. Thomson (Lord Kelvin). Thomson's researches on this subject commenced with one or two short investigations regarding the ponderomotive forces which act on temporary magnets. In 1847 he discussed[2] the case of a small iron sphere placed in a magnetic field, showing that it is acted on by a ponderomotive force represented by - grad cR2, where c denotes a constant, and R denotes the magnetic force of the field; such a sphere must evidently tend to move towards the places where R2 is greatest. The same analysis may be applied to explain why diamagnetic bodies tend to move, as in Faraday's experiments, from the stronger to the weaker parts of the field.
- ↑ We suppose all transitions to be continuous, so as to avoid the necessity for writing surface-integrals separately.
- ↑ Camb. and Dub. Math. Journal, ii (1847), p. 230; W. Thomson's Papers on Electrostatics and Magnetism, p. 499; cf. also Phil. Mag. xxxvii (1850), p. 241.
R 2
