Hans Christian Oersted

In 1807, Hans Christian Oersted (b. 1777, d. 1851), Professor of Natural Philosophy in Copenhagen, announced his intention of examining the action of electricity on the magnetic needle; but it was not for some years that his hopes were realized.

If one of his pupils is to be believed,[33] he was “a man of genius, but a very unhappy experimonter; he could not manipulate instruments. He must always have an assistant, or one of his auditors who had easy hands, to arrange the experiment.”

During a course of lectures which he delivered in the winter of 1819-20 on “Electricity, Galvanism, and Magnetism,” the idea occurred to him that the changes observed with the compass-needle during a thunderstorm might give the clue to the effect of which he was in search.

This led him to think that the experiment should be tried with the galvanic circuit closed instead of open, and to inquire whether any effect is produced on a magnetic needle when an electric current is passed through a neighbouring wire.

At first he placed the wire at right angles to the needle, but observed no result.

After the end of a lecture in which this negative experiment had been shown, the idea occurred to him to place the wire parallel to the needle: on trying it, a pronounced deflexion was observed, and the relation between magnetism and the electric current was discovered. After confirmatory experiments with more powerful apparatus, the public announcement was made in July, 1820.[34]

Oersted did not determine the quantitative laws of the action, but contented himself with a statement of the qualitative effect and some remarks on its cause, which recall the magnetic speculations of Descartes.

Oersted’s conceptions may be regarded as linking those of the Cartesian school to those which were introduced subsequently by Faraday.

“To the effect which takes place in the conductor and in the surrounding space,” he wrote, “we shall give the name of the conflict of electricity.”

“The electric conflict acts only on the magnetic particles of matter. All non-magnetic bodies appear penetrable by the electric conflict, while magnetic bodies, or rather their magnetic particles, resist the passage of this conflict. Hence they can be moved by the impetus of the contending powers.

“It is sufficiently evident from the preceding facts that the electric conflict is not confined to the conductor, but dispersed pretty widely in the circumjacent space.

“From the preceding facts we may likewise collect, that this conflict performs circles; for without this condition, it seems impossible that the one part of the uniting wire, when placed below the magnetic pole, should drive it toward the east, and when placed above it toward the west; for it is the nature of a circle that the motions in opposite parts should have an opposite direction.”

Oersted’s discovery was described at the meeting of the French Academy on September 11, 1820, by an academician (Arago) who had just returned from abroad.

Several investigators in France repeated and extended his experiments. The first precise analysis of the effect was published by two of these, Jean-Baptiste Biot (b. 1774, d. 1862) and Félix Savart (b.1791, d. 1841), who, at a meeting of the Academy of Sciences on October 30t, 1820, announced[35] that the action experienced by a pole of austral or boreal magnetism, when placed at any distance from a straight wire carrying a voltaic current, may be thus expressed:

“Draw from the pole a perpendicular to the wire; the force on the pole is at right angles to this line and to the wire, and its intensity is proportional to the reciprocal of the distance.”

This result was soon further analysed, the attractive force being divided into constituents, each of which was supposed to be due to some particular element of the current; in its new form the law may be stated thus: the magnetic force due to an element ds of a circuit, in which a current i is flowing, at a point whose vector distance from ds is r, is (in suitable units)

It was now recognized that a magnetic field may be produced as readily by an electric current as by a magnet; and, as Arayo soon showed,[38] this, like any other magnetic field, is capable of inducing magnetization in iron.

The question naturally suggested itself as to whether the similarity of properties between currents and magnets extended still further, e.g. whether conductors carrying currents would, like magnets, experience ponderomotive forces when placed in a magnetic field, and whether such conductors would consequently, like magnets, exert ponderomotive forces on each other.

The first step towards answering these inquiries was taken by Oersted[39] himself. “As,” he said, “a body cannot put another in motion without being moved in its turn, when it possesses the requisite mobility, it is easy to foresee that the galvanic arc must be moved by the magnet”; and this he verified experimentally.

The next step came from André Marie Ampère (b. 1775, d. 1836), who at the meeting of the Academy on September 18th, exactly a week after the news of Oersted’s first discovery had arrived, showed that two parallel wires carrying currents’ attract each other if the currents are in the same direction, and repel each other if the currents are in opposite directions. During the next three years Ampère continued to prosecute the researches thus inaugurated, and in 1825 published his collected results in one of the most celebrated memoirs[40] in the history of natural philosophy.

Ampère introduces his work by proclaiming himself a follower of that school which explained all physical phenomena in terms of equal and oppositely directed forces between pairs of particles; and he renounces the attempt to seek more speculative, though possibly more fundamental, explanations in terms of the motions of ultimate fluids and aethers. Nevertheless, he indicates two conceptions of this latter character, on which such explanations might be founded.

In the first[41] he suggests that the ponderomotive forces between circuits carrying electric currents may be due to “the reaction of the elastic fluid which extends throughout all space, whose vibrations produce the phenomena of light,” and which is “put in motion by electric currents.”

This fluid or aether can, he says, “be no other than that which results from the combination of the two electricities.”

In the second conception,[42] Ampère suggests that the interspaces between the metallic molecules of a wire which carries a current may be occupied by a fluid composed of the two electricities, not in the proportions which form the neutral fluid, but with an excess of that one of them which is opposite to the electricity peculiar to the molecules of the metal, and which consequently masks this latter electricity.

In this inter-molecular fluid the opposite electricities are continually being dissociated and recombined; a dissociation of the fluid within one inter-molecular interval having taken place, the positive electricity thus produced unites with the negative electricity of the interval next to it in the direction of the current, while the negative electricity of the first interval unites with the positive electricity of the next interval in the other direction, Such interchanges, according to this hypothesis, constitute the electric current.

Ampère’s memoir is, however, but little occupied with the more speculative side of the subject. His first aim was to investigate thoroughly by experiment the ponderomotive forces on electric currents.

“When,” he remarks, “M. Oersted discovered the action which a current exercises on a magnet, one might certainly have suspected the existence of a mutual action between two circuits carrying currents; but this was not a necessary consequence; for a bar of soft iron also acts on a magnetized needle, although there is no mutual action between two bars of soft iron.”

Ampère, therefore, submitted the matter to the test of the laboratory, and discovered that circuits carrying electric currents exert ponderomotive forces on each other, and that ponderomotive forces are exerted on such currents by magnets.

To the science which deals with the mutual action of currents he gave the name electro-dynamics;[43] and he showed that the action obeys the following laws:

1. The effect of a current is reversed when the direction of the current is reversed.
2. The effect of a current flowing in a circuit twisted into small sinuosities is the same as if the circuit were smoothed out.
3. The force exerted by a closed circuit on an element of another circuit is at right angles to the latter.
4. The force between two elements of circuits is unaffected when all linear dimensions are increased proportionately, the current-strengths remaining unaltered.

From these data, together with his assumption that the force between two elements of circuits acts along the line joining them, Ampère obtained an expression of this force: the deduction nay be made in the following way:—

Let:

• ds, ds′ be the elements
• r the line joining them
• i, i′ the current-strengths.

From (2) we see that the effect of ds on ds′ is the vector sum of the effects of dx, dy, dz on ds′, where these are the three components of ds: so the required force must be of the form—

Γ x a scalar quantity which is linear and homogeneous in ds; and it must similarly be linear and homogeneous in ds′; so using (1), we see that the force must be of the form

where φ and ψ denote undetermined functions of r.

From (4) it follows that when ds, ds′’, r are all multiplied by the same number, F is unaffected: this shows that

…

where A and B denote constants. Thus we have

…

Now, by (3), the resolved part of F along ds′ must vanish when integrated round the circuit s, i.e. it must be a complete differential when dr is taken to be equal to -ds. That is to say,

…

must be a complete differential; or

..

must be a complete differential; and therefore

Thus finally we have

…

This is Ampère’s formula: the multiplicative constant depends of course on the units chosen, and may be taken to be - 1.