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Current Electricity


CURRENT ELECTRICITY The electrical phenomena so far considered have been almost entirely such as depend on the attractions and repulsions be tween charges on conductors. The movement of these charges along the conductors will now be considered.


In 1780 Luigi Galvani (1737-1798) of Bologna dis covered a new type of electrical phenomena. He was studying frogs' nerves, and had dissected and prepared a frog which was laid on a table on which was an electric machine. It was noticed that, if the nerves of the frog were touched with a scalpel and, at the same moment, a spark was taken from the machine, the frog's legs were violently convulsed. Galvani found that lightning flashes pro duced the same effect. A little later he found that, if the feet of a dead frog, supported by a brass wire driven into its spinal marrow, were allowed to touch an iron plate, when the brass wire also touched the plate the frog's legs contracted suddenly. Galvani found that the same effect could be produced with any other pair of metals besides brass and iron but that electrical insulators gave no such effect. He found that the contractions were produced when the wire in the spinal marrow was connected to the plate on which the frog's feet rested by any conductors. Galvani considered that when the wire and plate were connected there was a flow of electricity from the nerves to the muscles of the frog which caused the muscles to contract.


These phenomena were investigated by Alessandro Volta (1745-1827) who supposed that the flow of electricity was due to the contact of the two different metals, e.g., brass and iron when connected by a moist conductor such as the frog's body. He found that powerful electric effects could be produced by a series of such metallic pairs. He made a pile of a large number of cop per, zinc and moist paper discs arranged in the following order : Copper, zinc, paper, copper, zinc, paper, copper, zinc, paper and so on. Volta found that if the bottom and top discs were touched one with each hand a distinct shock was felt not unlike that of a Leyden jar but that the sensation continued as long as the pile was touched. In the series of discs, (+) Cu, Zn, P, Cu, Zn, P, . . . Cu, Zn, P (—), the left hand end was positively charged and right end negatively charged. The fact that this is so could be demonstrated by connecting either end to an electroscope. It was found that if the paper discs were moistened with dilute acids or salt solutions the electrical effects were intensified. Volta pub lished his discovery in 180o.


In the same year (i800) Nicholson and Carlisle in England while repeating Volta's experiments found that if two wires connected to the ends of the pile were dipped into water hydrogen gas was evolved from the negative wire and the positive wire became oxydized. Using platinum wires they obtained hydro gen from the negative wire and oxygen from the positive wire. It appeared that the electricity flowing through the water from the one wire to the other decomposed it into its elements in such a way that they appeared separately one at each wire, whatever the distance between the wires. Such decompositions are called elec trolysis.

Cruickshank (1745-180o) soon afterwards found that metallic salts in solution can be decomposed in the same way. For exam ple, with a solution of copper sulphate, copper is deposited on one wire, and sulphuric acid and oxygen appear at the other. Wollas ton (1766-1828) showed that the same decompositions on a very small scale could be produced by electricity from a frictional ma chine, and in 18o' Pfaff (1773-1852) showed that a Leyden jar could be charged by means of a Voltaic pile having a very large number of elements. Thus the identity of frictional and Voltaic electricity was established.

Humphry Davy (1778-1829) studied the action of Voltaic piles, and concluded that chemical action on the zinc accompanies the generation of electricity, and is in some way the cause of it. Davy and Grothus explained the decomposition of water and other bodies by supposing that hydrogen atoms in water molecules are positively charged, and the oxygen atoms negatively. At the negatively charged wire hydrogen atoms are separated, giving up their positive charges to the wire. The oxygen atoms set free com bine with hydrogen atoms in other molecules, and the oxygen atoms from these with hydrogen atoms in still other molecules, and so on, until oxygen atoms appear at the positive electrode. Thus we may imagine a row of water molecules extending from the negative to the positive electrode. If now the hydrogen in each molecule moves into the next one in the row, the result is that we get free hydrogen at one end and free oxygen at the other.

This view was opposed by La Rive (1801-1873), who showed that metals could be made to pass from a salt solution through pure water to a negatively charged electrode. La Rive consid ered that salts in solution were partially dissociated into oppo sitely charged particles, and that the negative particles moved through the liquid to the positive electrode and the positive parti cles to the negative electrode. These electrolytic decompositions led Berzelius 0779-1848) to propose a theory of chemical affinity according to which the atoms in the molecules of compounds are oppositely charged and are held together by electrical attraction.

Magnetic Field Currents.

In 1820 a new discovery of the first magnitude turned the progress of electrical science into a new direction. Hans Christian Oersted (1777-1851) discovered that a wire carrying a current exerts a force on a magnet, or produces a magnetic field. He found that, if the wire is placed in the meridian, above a compass needle, when a current flows in the wire from south to north, the north pole of the needle is deflected towards the west. The direction of the force on the north pole was along circles in planes perpendicular to the wire with their centres at the wire. Oersted also found that the magnet exerted a force on the wire carrying the current.

This subject was taken up by Biot (1774-1862) and Savart (1791-1841) in France, and then by Ampere (1775-1836). Am pere one week after the news of Oersted's discovery arrived in Paris, showed that two parallel wires, carrying currents in the same direction, attract each other, but repel when the currents are in opposite directions. During the next few years Ampere investi gated the subject experimentally and mathematically, and in 1825 published an account of his researches in a memoir which has ex cited the admiration of mathematicians and physicists ever since. He showed that the forces, between currents and magnets, and between one current and another, could be represented by sup posing that each element of a circuit exerts a force on a magnetic pole and on every other current element.

A current element of length ds at a point 0 carrying a current i produces a magnetic field of strength ids sin at a point P, where r=OP and 0 is the angle between the current element and OP. The direction of this field is perpendicular to the plane con taining ds and OP. The force on a current element in a magnetic field of strength H is equal to Hids sin where 4) is the angle between ds and H. This force is perpendicular to H and ds. Am pere assumed that the force between two current elements is along the line joining them. This assumption is not now believed to be correct, but his theory nevertheless gave correct results for the force exerted by one circuit on another. Ampere called the theory of the mutual action of currents electrodynamics.

Thermoelectricity and Ohm's Law.

In 1822, Seebeck (177o-1831) of Berlin discovered that a current is produced in a circuit of two metals when one of the junctions is made hotter than the other one. This discovery initiated the branch of elec tricity known as thermoelectricity. In 1834 Peltier (1785-1845) discovered that, when a current is passed across a junction between two metals, heat is absorbed when the current is in one direction and evolved when it is in the other direction.

In 1826 Georg Simon Ohm (1787-1854) published a paper on the flow of electricity through conducting wires in which a result since known as Ohm's Law was established. Ohm argued that the flow of electricity along a wire was analogous to the flow of heat along a rod, one end of which was hotter than the other. The quantity of heat flowing per second is proportional to the difference of temperature, so Ohm suggested that there must be an electrical quantity, analogous to temperature, concerned. He showed that this quantity, which he called electroscopic force, increases by equal increments on passing from one copper plate of a Voltaic pile to the next. This shows that Ohm's electroscopic force is the same thing as electrostatic potential difference. Ohm showed that the current through a wire is equal to the electroscopic force act ing on the wire multiplied by a constant. This constant is now called the conductivity of the wire and its reciprocal the resistance. The resistance is proportional to the length and varies inversely as the cross section of the wire. The resistance of a wire of unit length and unit cross section is called the specific resistance of the material of the wire.

Electromagnetic Induction of Currents.

Soon after Oer sted's discovery of the magnetic field of currents Faraday began an investigation of the subject. It occurred to him that an effect analogous to electrostatic induction of charges on conductors might be produced by currents, i.e., a current flowing in a circuit might induce a current in another circuit near it. Oersted's discovery shows that a current excites a field in the surrounding space which might be expected to produce effects on bodies in it. In 1831, Far aday found that, when a current is started in a coil of wire, a momentary current is induced in another near-by coil. When the primary current is stopped, an induced current is again obtained but in the opposite direction. He showed that the effect is due to the magnetic field of the primary current, and that the induced current in any circuit is proportional to the rate of change of the number of unit tubes of magnetic force passing through the cir cuit. He mounted a copper disc between the poles of a magnet, so that the tubes of force passed through the disc. The axle of the disc and a point on its circumference were connected by sliding contacts to wires leading to a galvanometer, and, when the disc was made to rotate with uniform velocity, the galvanometer indi cated a steady current. This apparatus was the first dynamo, or electric generator, and all the generators now used for the produc tion of currents for technical purposes work on the same principle.

The mathematical theory of electromagnetic induction of cur rents was developed by Neumann and Weber (1804-1890) . It was shown by Neumann that the mutual potential of two circuits is equal to the number of unit tubes of magnetic force, due to one of them, which pass through the other one multiplied by the cur rent in it. According to Faraday's law, the currents induced de pend on the variation of this quantity, so that the induced currents can be calculated from the mutual potential energy. Weber sup posed that a current in a wire consists of a flow of positively charged particles in one direction, together with an equal flow of negative particles in the opposite direction. He deduced an ex pression for the force exerted by one such particle on another one at any distance, and showed that the mutual action of circuits including the induced currents could be explained in this way. Weber's law of force gave correct results, in many cases, but it has been replaced by other conceptions in the modern theory. Weber's idea that a current consists of a flow of particles of electricity reappeared at a much later date in the modern electron theory.

Faraday's Laws of Electrolysis.

In 1833, Faraday published a series of researches on electrolysis. He found that the amount of any element deposited at the electrodes is proportional to the quantity of the electricity passed through the electrolyte. Also, the amount deposited by a given q lantity of electricity is propor tional to the atomic weight divided by the chemical valency. Thus, if a certain quantity of electricity deposits one gram of hydrogen, it will deposit 8 grams of oxygen and 108 grams of silver. The atomic weights of these elements being 1,16 and 108, and the valencies I, 2 and 1, respectively. Faraday pointed out that this result showed that all monovalent atoms in solution carry the same charge of electricity, the charge now called the ionic charge, and that divalent atoms carried twice and trivalent atoms three times this ionic charge. Faraday called the wires or plates by means of which the current was passed through the liquid to be electrolysed the electrodes. The positive electrode he named the anode and the other the cathode. Bodies which are de composed when a current is passed through them he called elec trolytes, and the parts into which they are decomposed, which move towards the electrodes, ions. Faraday supposed that chemi cal affinity is due to the charges carried by the atoms, a positively charged atom combining with a negatively charged one.


question which had been discussed ever since Volta's pile was discovered was the nature of the forces which cause the flow of electricity when the ends of the pile are connected. Volta showed that when a copper plate and a zinc plate are put in con tact and then separated they are oppositely charged, and he con sidered that the driving force in his pile was at the junction be tween the two metals used. When it was found that chemical action accompanies the flow of electricity through electrolytes, so that in the pile there is chemical action between the zinc and the acid or salt solution by which zinc is dissolved, it was suggested that the chemical affinity between the zinc and the solution is the source of the chemical energy. If a plate of pure zinc and one of copper are placed in dilute sulphuric acid so that they do not touch each other, the zinc does not dissolve in the acid ; but, if the two plates are connected by a wire, the zinc begins to dissolve and hydrogen gas is liberated at the surface of the copper plate. A current flows through the wire, from the copper to the zinc, and, through the acid, from the zinc to the copper. The chemical action is represented by the equation Zn+H.,SO,=ZnSOd-H.,, and the amount of zinc dissolved and hydrogen liberated are determined by the amount of electricity which flows round the circuit, in ac cordance with Faraday's laws of electrolysis.

It was argued by Peter Roget (1779-1869), and later by Fara day and La Rive, that the electrical energy supplied by such a cell or element of a Voltaic pile must come from the chemical affinity between the acid and zinc which combine in the cell. If the current merely came from the contact between two metals, Faraday said, it would be a "creation of power like no other force in nature." Magnetism and Light.—In 1845 Faraday placed a block of glass between the poles of a powerful magnet and then passed a beam of plane polarized light through the block along the direc tion of the magnetic field. He found that the plane of polariza tion of the light was rotated as it passed through the glass. By this discovery the sciences of electricity and magnetism were linked with optics. Faraday discussed the nature of light waves, suggesting that they might turn out to be transverse vibrations travelling along his lines of electric and magnetic force. He thus brilliantly foreshadowed the electromagnetic theory of light, which was afterwards worked out by Clerk Maxwell largely as the result of a translation of Faraday's ideas into mathematical form. Faraday, in 1845, also discovered that all substances have mag netic properties in greater or less degree. Some bodies tend to move, in a magnetic field, towards the stronger parts of the field ; these Faraday called paramagnetic bodies. Other bodies, notably bismuth, he found tend to move into the weaker parts of the field ; these he called diamagnetic bodies. Faraday's experimental work ended in 18J5 when he retired. He died in 1867. His col lected scientific papers, published in four volumes, form a note worthy monument to the greatest of all experimental philosophers.

In 1847, Weber showed that diamagnetism could be explained by supposing that currents are induced in the molecules of dia magnetic bodies when they are placed in a magnetic field. Ampere had previously suggested that the magnetic properties of iron atoms may be due to currents flowing round small circuits in the atoms. Weber supposed that paramagnetic atoms have such cur rents always, but that diamagnetic atoms normally have no cur rents but acquire them when put in a magnetic field. The induced currents produce a field opposite to the inducing field so that the resultant field in diamagnetic bodies is less than in non-magnetic bodies. In paramagnetic bodies there is no resultant field when they are not magnetized because the atomic circuits are orientated at random. When put in a field, the atomic circuits tend to turn so that their fields are in the same direction as the inducing field, so giving a resultant field greater than that in a non-magnetic body. (See MAGNETISM.) Electricity and the Conservation of Energy.—The prin ciple of the conservation of energy was finally placed on a solid foundation about 1841 by the labours of James Prescott Joule of Manchester. He applied it to electrical circuits, and showed that the chemical energy, used up in a battery sending a current through a wire, was approximately equivalent to the heat generated in the circuit by the flow of the current. He showed that the heat generated in a wire was proportional to the square of the current in it.

Helmholtz (1821-1894) in 1842 showed that the chemical energy used up in a battery may not be exactly equal to the electrical energy developed, because some heat energy may be absorbed from surrounding bodies. In 1847 Helmholtz published a great memoir, on the conservation of energy, in which he applied the principle to electrostatic and magnetic problems among others. He calculated the electric and magnetic energies by assuming that the work required to produce the final state was stored up in the system. He showed that the energy of a system of charged conductors is equal to IL EV where E is the charge and V the potential of a conductor. The potential is the function, used by Poisson and Green, which is equal to the work required to bring a unit charge from a great distance to the conductor. Helmholtz also considered systems involving currents, and showed that the existence of Faraday's induced currents followed from the prin ciple of the conservation of energy.

The theory of the energy of electromagnetic systems was

worked out by William Thomson (Lord Kelvin) in a series of papers (1847-1853). He defined the strength of the magnetic field inside a piece of iron as the force on a unit pole put in a long hole bored in the iron along its direction of magnetization. The magnetic induction in the iron he defined as the field strength in a slot cut across the direction of magnetization. The ratio of the magnetic induction to the field strength is the permeability of the iron. Thomson showed that the magnetic energy could be regarded as distributed throughout the field with density p. where is the permeability and H the field strength.

He showed that the energy of the magnetic field of a circuit

carrying a current i, in air, is equal to Ni,L where N is the number of unit tubes of magnetic force passing through the circuit. N is proportional to i so that if we put N=Si we get for the energy. The quantity S=N/i is called the self induction of the circuit.

In 1848 Kirchhoff (1824-1887) discussed the theory of the

flow of currents in conductors, basing his theory on Ohm's law. He finally identified Ohm's electroscopic force with electrostatic potential difference, the work required to move a unit charge from one point in the electric field to another. The electromotive force in a circuit is the work required to move a unit charge once round the circuit. Ohm's law therefore means that the current in a circuit is proportional to the electromotive force acting in the circuit. The resistance of the circuit is defined to be the ratio of the electromotive force to the current.

Oscillatory Discharges.

In 1853 Thomson (Lord Kelvin) published a theory of the discharge of a Leyden jar, which was of fundamental importance. Several observers, Wollaston (18o1), Savary (1827), Joseph Henry (1842) and Helmholtz, had sug gested that when a jar is discharged the electricity oscillates backwards and forwards from one coating of the jar to the other. These suggestions were based on observations of effects produced by the discharge. For example, Wollaston found that, when a jar is discharged through water between two wires, oxygen and hydro gen appear on both wires, as if the current went both ways through the water.

Lord Kelvin supposed that the current, in a wire connecting

the two coatings, is proportional to the potential difference be tween the coatings less the induced electromotive force in the wire, due to its self induction. When the jar is charged and there is no current in the wire, the energy is all electrostatic energy, but when the jar is discharged and there is a current in the wire, the energy is all magnetic energy of the field of the current. The energy changes from electric to magnetic and back again, just as when a pendulum oscillates the energy changes from potential to kinetic and back again.

Kelvin showed that the discharge should be oscillatory and

that the periodic time is CS, where C is the capacity of the jar and S the self induction of the wire. The number of oscilla tions per second with an ordinary jar and a short wire is very large, of the order of ten millions. It was soon afterwards shown by Fedderson that the spark, that occurs when a jar is discharged, is really a series of sparks. He examined the spark in a rapidly rotating mirror and so was able to see the successive sparks separately. The time between the sparks agreed with that given by Kelvin's theory.

Kelvin also worked out the theory of the propagation of elec trical signals along long wires, such as submarine cables, and in 1857 Kirchhoff worked out the propagation of an electrical dis turbance along a wire in air, and showed that the velocity of prop agation, in centimetres per second, should be equal to the ratio of the electromagnetic unit of electricity to the electrostatic unit. This ratio had been found experimentally, by Weber and Kohl rausch in 1856, to be equal to 3.1 X which is nearly equal to the velocity of light in centimetres per second. Thus it appeared, as Kirchhoff pointed out, that the velocity of propagation of an electric disturbance along a wire in air is equal to the velocity of light in air.

In 1851 Kelvin worked out the thermodynamical theory of

thermoelectricity, and discovered that there is an absorption or an evolution of heat in a wire when there is a temperature gradient and a current of electricity along it. The heat absorbed per unit quantity of electricity per unit rise of temperature was called the specific heat of electricity in the wire. It is positive in some metals and negative in others.

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