OERSTED’S DISCOVERY

153*.] Oersted discovered that a magnet placed near a straight electric current tends to place itself at right angles to the plane passing through the magnet and the current.

If a man were to place his body in the line of the current so that the current from copper through the wire to zinc should flow from his head to his feet, and if he were to direct his face towards the centre of the magnet, then that end of the magnet which tends to point to the north would, when the current flows, tend to point towards the man’s right hand. Thus we see that the elec- tric current has a magnetic action which is exerted outside the current, and by which its existence can be ascertained and its intensity measured without breaking the circuit or introducing anything into the current itself. The amount of the magnetic action has been ascertained to be strictly pro- portional to the strength of the current as measured by the products of elec- trolysis in the voltameter, and to be quite independent of the nature of the conductor in which the current is flowing, whether it be a metal or an electrolyte.

154*.] An instrument which indicates the strength of an electric current by its magnetic effects is called a Galvanometer.

Galvanometers in general consist of one or more coils of silk-covered wire within which a magnet is suspended with its axis horizontal. When a current is passed through the wire the magnet tends to set itself with its axis perpendicular to the plane of the coils. If we suppose the plane of the coils to be placed parallel to the plane of the earth’s equator, and the current to flow round the coil from east to west in the direction of the apparent motion of the sun, then the magnet within will tend to set itself with its magnetization in the same direction as that of the earth considered as a great magnet, the north pole of the earth being similar to that end of the compass needle which points south.

The galvanometer is the most convenient instrument for measuring the strength of electric currents. We shall therefore assume the possibility of constructing such an instrument in studying the laws of these currents, and when we say that an electric current is of a certain strength we suppose that the measurement is effected by the galvanometer.

On Systems of Linear Conductors.

155*.] Any conductor may be treated as a linear conductor if it is arranged so that the current must always pass in the same manner between two por- tions of its surface which are called its electrodes. For instance, a mass of metal of any form, the surface of which is entirely covered with insulating material except at two places, at which the exposed surface of the conductor is in metallic contact with electrodes formed of a perfectly conducting mate- rial, may be treated as a linear conductor. For if the current be made to enter at one of these electrodes and escape at the other the lines of flow will be determinate, and the relation between electromotive force, current, and resis- tance will be expressed by Ohm’s Law, for the current in every part of the mass will be a linear function of E. But if there be more possible electrodes than two, the conductor may have more than one independent current through it.

Ohm’s Law.

156*.] Let E be the electromotive force in a linear conductor from the electrode A1 to the electrode A2 . (See Art. 5.) Let C be the strength of the electric current along the conductor, that is to say, let C units of electricityRESISTANCE OF CONDUCTORS IN SERIES.

pass across every section in the direction A1 A2 in unit of time, and let R be the resistance of the conductor, then the expression of Ohm’s Law is E = CR. (1)

The Resistance of a conductor is defined to be the ratio of the electromotive force to the strength of the current which it produces. The introduction of this term would have been of no scientific value unless Ohm had shewn, as he did experimentally, that it corresponds to a real physical quantity, that is, that it has a definite value which is altered only when the nature of the conductor is altered.

In the first place, then, the resistance of a conductor is independent of the strength of the current flowing through it.

In the second place the resistance is independent of the electric potential at which the conductor is maintained, and of the density of the distribution of electricity on the surface of the conductor.

It depends entirely on the nature of the material of which the conductor is composed, the state of aggregation of its parts and its temperature. The resistance of a conductor may be measured to within one ten thou- sandth or even one hundred thousandth part of its value, and so many con- ductors have been tested that our assurance of the truth of Ohm’s Law is now very high∗ .

Linear Conductors arranged in Series.

157*.] Let A1 , A2 be the electrodes of the first conductor and let the second conductor be placed with one of its electrodes in contact with A2 , so that the second conductor has for its electrodes A2 , A3 . The electrodes of the third conductor may be denoted by A3 and A4 .

Let the electromotive force along each of these conductors be denoted by E12 , E23 , E34 , and so on for the other conductors.

Let the resistance of the conductors be R12 , ∗ R23 , R34 , [See Report of British Association, 1876.]

&c.RESISTANCE OF CONDUCTORS IN SERIES.

Then, since the conductors are arranged in series so that the same current C flows through each, we have by Ohm’s Law, E12 = CR12 , E23 = CR23 , E34 = CR34 . (2) If E is the resultant electromotive force, and R the resultant resistance of the system, we must have by Ohm’s Law, E = CR. (3) Now E = E12 + E23 + E34 , (4) the sum of the separate electromotive forces, = C(R12 + R23 + R34 ) by equations (2). Comparing this result with (3), we find R = R12 + R23 + R34 (5) Or, the resistance of a series of conductors is the sum of the resistances of the conductors taken separately. Potential at any Point of the Series. Let A and C be the electrodes of the series, B a point between them, a, c, and b the potentials of these points respectively. Let R1 be the resistance of the part from A to B, R2 that of the part from B to C, and R that of the whole from A to C, then, since a − b = R1 C, b − c = R2 C, and a − c = RC, the potential at B is R2 a + R 1 c , R which determines the potential at B when those at A and C are given. b=

(6)RESISTANCE OF CONDUCTORS IN MULTIPLE ARC. 143