Faraday's law of induction

In the following paragraph,¹⁾ published in 1832, Faraday described one of the numerous experiments through which he developed his ideas of induced emf:

Two hundred and three feet of-copper wire in one length were passed round a large block of wood; other two hundred and three feet of similar wire were interposed as a spiral between the turns of the first coil, and metallic contact everywhere prevented by twine.* One of these helices was connected with a galvanometer, and the other with a battery of one hundred pairs of plates of four inches square, with double coppers, and well charged. When the contact was made, there was a sudden and very slight effect at the galvanometer, and there was also a similar slight effect when the contact with the battery was broken. But whilst the voltaic current was continuing to pass through the one helix, no galvanometrical appearances nor any effect like induction upon the other helix could be perceived, although the active power of the battery was proved to be great, by its heating the whole of its own helix, and by the brilliancy of the discharge when made through charcoal.

He summarizes the results of a whole group of such experiments involving both changing currents and moving magnets, in the following short paragraph,²⁾ which, allowing for a considerable change in nomenclature since his time, we see refers to the existence of induced emf:

All these results show that the power of inducing electric currents is circumferentially excited by a magnetic resultant or axis of power, just as circumferential magnetism is dependent upon and is exhibited by an electric current.

Faraday developed a general description of the time-varying events which result in induced emf. He found, as we can easily show by experiment, that the emf induced in any loop depends only on the time rate of change of the flux of magnetic field surrounded by the circuit. This idea can be expressed by the equation

E = – dΦ/dt volts (9.1)

where E is the induced emf, and Φ the magnetic flux, ∫B・dS, as in Eq. (8.19), which threads the circuit. The integration is over the area surrounded by the circuit. We comment later on the negative sign used in Eq. (9.1).

To illustrate the generality of Faraday's law let us consider a - - - -

1) Michael Faraday, Experimental Researches in Electricity, Phil. Trans. Roy.

Soc. London, 122A: 127, 155 (1832).

2) Ibid.

* 麻糸