## Oersteds discovery

At about the same time as Coulomb was making his discoveries, a Danish scientist, Hans Christian Oersted (1777-1851), was also experimenting with electrical currents. Oersted gave a public lecture in April 1820 in which he demonstrated that an electric current could be produced in a wire by means of a battery. The wire began to glow as its temperature increased, showing

Hans Christian Oersted

that the current was generating heat and light. As he was giving the lecture, it struck him that there might be some magnetic effect associated with the current. As it happened, there was a magnetic compass needle to hand, which he brought over and placed under the wire. Perhaps it would align itself along the wire? Apart from a barely noticeable sideways twitch, nothing much seemed to happen. The audience became a little restive, so Oersted put aside his equipment and continued with the lecture. He had broken the cardinal rule that one should never try a public demonstration of anything which has not been tried beforehand!

Later, in the privacy of his laboratory, he tried again. This time he used a stronger current and the effect on the needle became more visible. It turned in a direction perpendicular to the current. Oersted could only come to one conclusion: there was a connection between electricity and magnetism. It became clear that a fundamental rnmmsmm

l discovery had been made, probably for the first and last time in the history of science, in front of a live audience!

In the months after Oersted's discovery there followed great activity in the study of the magnetic effect of electric current. Ampère refined Oersted's experiments and found that the magnetic lines of

Iron filings around a current-carrying wire. Courtesy of James Ellis, UCD School of Physics.

force formed circles around the current-carrying wire in a plane perpendicular to the wire.

Two French physicists, Jean-Baptiste Biot (1774-1862) and Felix Savart (1791-1841), devised a mathematical formula for the magnitude and direction of this magnetic field in the vicinity of a current-carrying wire. According to the Biot-Savart law, at the point P, the magnitude of the contribution to the magnetic field dB due to the section dl of wire carrying a current i is dB = 0

I i dl sind

4nr2

Figure 10.12 The Biot-Savart law.

Applying this formula to an 'infinitely long' straight wire shows that a current i in such a wire gives rise to a magnetic field which can be represented by a series of rings which encircle the wire, as illustrated below. The magnitude of the magnetic field B at a perpendicular distance r from the wire is

The magnetic field is measured in teslas, (T) a unit named after the Serbian scientist Nikola Tesla (1856-1943). ¡0is called the magnetic constant, or permeability. Its value in SI units is by definition m0 = 4^ x 10-7 Tm/A *

* We may also write ¡¡0 = 4n x 10-7 newtons/A2; a summary of the logical order in which the units of current, charge and magnetic field are defined is given in Appendix 10.2.

It is interesting to note that, while the contribution of each segment of current decreases as the square of the distance to the point P, the magnetic field B produced by the whole infinite wire decreases as 1/R. The direction of B is at all times in a plane perpendicular to the current. This somewhat complicated relation between cause and effect results in magnetic field lines which form the aforementioned concentric circles around the wire, just as the iron filings would suggest.

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