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Electromagnetic Induction

Oersted’s discovery of the compass deflection by the electric current had great theoretical importance. In the hands of Ampere, Gauss and Ohm it led to the understanding of the magnetic fields produced by currents and the way they flowed through conductors. Electricity could now become a quantitative science and take over all the mathematical apparatus of mechanics. Nevertheless, in one important and puzzling respect the new laws differed from those of Newton. All the forces between bodies, that he considered, acted along the line joining their centres; but here a magnetic pole moved at right angles to the line joining it to the current-carrying wire. This was the first break from the simple scalar field theory, and opened the way to a more inclusive vector theory, where direction as well as distance counted. It was these physical discoveries that were to give a new impetus to mathematics.

Before the full interaction of electricity could be understood, still one more decisive step had to be taken. It had been shown how electric currents produced magnetism; it remained to show how magnetism could produce electric currents. This discovery, though it had to wait for another ten years, was not, like Oersted’s, accidental. It was the result of a deliberately planned research by Faraday. In 1831, in his fortieth year, Faraday showed that the relation between magnetism and electricity was dynamic and not static — that a magnet had to be moved near an electric conductor for the current to arise. This most important observation showed that not only was magnetism equivalent to electricity in motion, but also, conversely, electricity was magnetism in motion.

Thus both sets of phenomena could only be discussed in the new joint science of electromagnetism.

Faraday’s discovery was also of much greater practical importance than Oersted’s, because it meant that it was possible to generate electric currents by mechanical action, and conversely that it was possible to operate machinery by electric currents. Essentially, the whole of the heavy electrical industry was in Faraday’s discovery. However. Faraday himself had little inclination to move in the direction of practical application. He was concerned, as his notebooks show, with a long-range project of discovering the interrelations between all the “forces” that were known to the physics of his time — electricity, magnetism, heat, and light — and by a series of ingenious experiments he was in fact able to succeed in establishing every one of these, and to discover in the process many other effects the full explanation of which has had to wait till our time.

The formal translation of Faraday's qualitative intuitions into precise and quantitative mathematical equations required the genius of Clerk Maxwell, who summarized in a brief but informative form the whole of electromagnetic theory.

Oersted’s discovery of the compass deflection by the electric current had great theoretical importance. In the hands of Ampere, Gauss and Ohm it led to the understanding of the magnetic fields produced by currents and the way they flowed through conductors. Electricity could now become a quantitative science and take over all the mathematical apparatus of mechanics. Nevertheless, in one important and puzzling respect the new laws differed from those of Newton. All the forces between bodies, that he considered, acted along the line joining their centres; but here a magnetic pole moved at right angles to the line joining it to the current-carrying wire. This was the first break from the simple scalar field theory, and opened the way to a more inclusive vector theory, where direction as well as distance counted. It was these physical discoveries that were to give a new impetus to mathematics.

Before the full interaction of electricity could be understood, still one more decisive step had to be taken. It had been shown how electric currents produced magnetism; it remained to show how magnetism could produce electric currents. This discovery, though it had to wait for another ten years, was not, like Oersted’s, accidental. It was the result of a deliberately planned research by Faraday. In 1831, in his fortieth year, Faraday showed that the relation between magnetism and electricity was dynamic and not static — that a magnet had to be moved near an electric conductor for the current to arise. This most important observation showed that not only was magnetism equivalent to electricity in motion, but also, conversely, electricity was magnetism in motion.

Thus both sets of phenomena could only be discussed in the new joint science of electromagnetism.

Faraday’s discovery was also of much greater practical importance than Oersted’s, because it meant that it was possible to generate electric currents by mechanical action, and conversely that it was possible to operate machinery by electric currents. Essentially, the whole of the heavy electrical industry was in Faraday’s discovery. However. Faraday himself had little inclination to move in the direction of practical application. He was concerned, as his notebooks show, with a long-range project of discovering the interrelations between all the “forces” that were known to the physics of his time — electricity, magnetism, heat, and light — and by a series of ingenious experiments he was in fact able to succeed in establishing every one of these, and to discover in the process many other effects the full explanation of which has had to wait till our time.

The formal translation of Faraday's qualitative intuitions into precise and quantitative mathematical equations required the genius of Clerk Maxwell, who summarized in a brief but informative form the whole of electromagnetic theory.

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