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Induction of Electrical Currents

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A Student's Guide Through the Great Physics Texts

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Abstract

Michael Faraday (1791–1867) was born in Newington Butts, which is now part of London. He had little formal education beyond day school as a young boy. Yet from a position as apprentice to a bookbinder at the age of 14, Faraday would become the Superintendent and Director of the laboratory at the Royal Institution, where his careful experimental work on electro-magnetism laid the foundation for Maxwell’s electromagnetic theory of light. Faraday’s most significant discovery, and the topic of the reading selection below, was presented initially in his address to the Royal Society on November 24, 1831. Herein, he describes his attempts to obtain “electricity from ordinary magnetism.” The lecture begins with a brief reminder of how bodies held in electrical “tension”—we would say they have an electrical potential, or voltage, difference—induce an electrical polarization in nearby materials. Before proceeding, he explains how his work was inspired, at least in part, by Arago’s recently observed magnetic phenomena and by Ampère’s “beautiful theory” of magnets.

These considerations, with their consequence, the hope of obtaining electricity from ordinary magnetism, have stimulated me at various times to investigate experimentally the inductive effect of electric currents.

—Michael Faraday

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Notes

  1. 1.

    For biographical notes on Faraday, see, for instance, Bence, J., The life and letters of Faraday, Longmans, Green and Co., London, 1870.

  2. 2.

    Maxwell’s electromagnetic theory of light will be developed in Chap. 31 of the present volume.

  3. 3.

    Faraday’s final series of Christmas lectures are wonderfully clear and enjoyable to read. See Faraday, M., The Chemical History of a Candle: to which is added a Lecture on Platinum, Harper & Brothers, New York, 1861 and Faraday, M., A Course of Six Lectures on the Forces of Matter and Their Relations to Each Other, Richard Griffin and Company, London and Glasgow, 1860.

  4. 4.

    The rotation of light by a magnetic field is now called Faraday rotation. This is described by John Tyndall in his lectures on light; see Chap. 23 of the present volume.

  5. 5.

    See Chap. 29 for a discussion of diamagnetic materials, and how they differ from ordinary magnetic materials.

  6. 6.

    The use of the term “electric tension” for electrical potential difference survives today: overhead high-voltage power lines are sometimes still referred to as “high tension” lines.

  7. 7.

    See Faraday’s discussion of Arago’s wheel in Chap. 26 of the present volume.

  8. 8.

    Ampère discusses how permanent magnets may be understood in terms of circulating electrical currents at the end of the reading included in Chap. 8 of the present volume.

  9. 9.

    The relative position of an electric current and a magnet is by most persons found very difficult to remember, and three or four helps to the memory have been devised by M. Ampère and others. I venture to suggest the following as a very simple and effectual assistance in these and similar latitudes. Let the experimenter think he is looking down upon a dipping needle, or upon the pole of the earth, and then let him think upon the direction of the motion of the hands of a watch, or of a screw moving direct; currents in that direction round a needle would make it into such a magnet as the dipping needle, or would themselves constitute an electro-magnet of similar qualities; or if brought near a magnet would tend to make it take that direction; or would themselves be moved into that position by a magnet so placed; or in M. Ampère’s theory are considered as moving in that direction in the magnet. These two points of the position of the dipping-needle and the motion of the watch-hands being remembered, any other relation of the current and magnet can be at once deduced from it.

  10. 10.

    To avoid any confusion as to the poles of the magnet, I shall designate the pole pointing to the north as the marked pole; I may occasionally speak of the north and south ends of the needle, but do not mean thereby north and south poles. That is by many considered the true north pole of a needle which points to the south; but in this country it is often called the south pole.

  11. 11.

    A soft iron bar in the form of a lifter to a horse-shoe magnet, when supplied with a coil of this kind round the middle of it, becomes, by juxta-position with a magnet, a ready source of a brief but determinate current of electricity.

  12. 12.

    Georg Ohm, a German physicist, published the empirically discovered law named after him in 1827. An English translation of parts of this paper can be found in Magie, W. F. (Ed.), A Source Book in Physics, Harvard University Press, Cambridge, Massachusetts, 1963, pp. 456–472.

  13. 13.

    This equipment is readily available from most scientific supply companies. For example, I have used Sargent Welch’s primary and secondary coils (Item #CP32989-00), a galvanometer (Item #WLS30663-32) and an Elenco Regulated DC Power Supply (Item #CP32787-00).

  14. 14.

    We were introduced (anachronistically) to the concept of the magnetic field in Ex. 7.4; we will have much more to say about this in Chap. 28. Suffice it to say for the ti being that a magnetic field is a medium for communicating forces between magnetic bodies.

  15. 15.

    See the discussion of Lenz’s law in Ex. 25.4.

  16. 16.

    In Eq. 25.5, we have tacitly assumed that the magnetic field strength is the same throughout the entire area of the loop, \(A\). In many cases, however, the magnetic field is non-uniform. Then we must sum the contributions to the magnetic flux at the location of each of \(N\) tiny area elements, \(\Delta A_i\), which comprise the total area of the loop:

    $$ \Phi = \sum_{i=1}^{N} B_i \cdot \Delta A_i. $$

    In each \(\Delta A_i\), the magnetic field strength, \(B_i\), is approximately uniform. And in the limit that \(N \rightarrow \infty \) and \(\Delta A_i \rightarrow 0\), the above sum may be written as a surface integral over infinitesimal area segments; see Appendix A.

  17. 17.

    The magnetic field around a long straight wire obeys the right hand rule; see Ex. 7.4 in the present volume.

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Correspondence to Kerry Kuehn .

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Kuehn, K. (2016). Induction of Electrical Currents. In: A Student's Guide Through the Great Physics Texts. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-21816-8_25

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