Magnetic flux

“ The practical electrical engineer, up to the present, prefers to use one ampere-turn as his unit of magnetomotive force, and one line of force as the unit of magnetic flux, equal respectively to 10/4π times and 1 times the C.G.S. absolute units. Very frequently the “kiloline,” equal to 1000 lines of force, is now used as a unit of magnetic flux. ”

“ In Quaternion language, the one vector is said to be a linear and vector function of the other, and when there are three pairs of equal coefficients the function is said to be self-conjugate.
In the case of magnetic induction in iron, the flux, (the magnetization of the iron,) is not a linear function of the magnetizing force. In all cases, however, the product of the force and the flux resolved in its direction, gives a result of scientific importance, and this is always a scalar quantity. ”

“ It had for its moving-member a magnetic field that varied on a pure sine wave of intensity from a terrific flux-density in one direction, through zero, and thence to an equally terrific flux-density in the opposite polarity. At one newspaper interview as the machine was being built some reporter had erroneously noted that the magnetic field strength at maximum was strong enough to affect the iron in your blood. ”

“ As the pull of an electromagnet upon its armature depends on the total number of lines of force passing from the core to the armature—that is, on the total flux—and as the total flux depends for a given magnetizing force on the reluctance of the magnetic circuit, it is obvious that the design of the electromagnetic circuit is of great importance in influencing the action of the magnet. ”

“ A thermal current (one produced by heat) of electricity seems to flow around the earth caused by the irregularities of temperature at the earth's surface, as the sun makes his daily round. These earth currents vary at times, and other phenomena are the occasion. This will be discussed when we come to electric storms.
The value of the earth's magnetism is seen most in the science of navigation. A magnetic needle is only a slender permanent magnet suspended very delicately, and when not under local influence it points north and south on the magnetic axis. ”

“ This ether pressure produced by a magnet may be as great as a ton per square inch. It is this pressure that holds an armature to the magnet. As heat is a molecular condition of vibration, and radiant energy the result of it, so is magnetism a property of molecules, and the magnetic field the temporary condition in the ether, which depends upon the presence of a magnetic body. We no longer speak of the wave-motion in the ether which results from heat, as heat, but call it radiation, or ether waves, and for a like reason the magnetic field ought not to be called magnetism. ”

“ If, therefore, by the motion of magnets or variations of currents in the neighbourhood, the magnetic field is in any way altered, electric currents will be set up in the current-sheet, such that their magnetic effect, combined with that of the magnets or currents in the field, will maintain the normal component of magnetic induction at every point of the sheet unchanged. If at first there is no magnetic action, and no currents in the sheet, then the normal component of magnetic induction will always be zero at every point of the sheet. ”

“ Now the magnet when employed in the deflexion experiments is placed with its axis east and west, so that the action of terrestrial magnetism is transverse to the magnet, and does not tend to increase or diminish . When the magnet is made to vibrate, its axis is north and south, so that the action of terrestrial magnetism tends to magnetize it in the direction of the axis, and therefore to increase its magnetic moment by a quantity , where is a coefficient to be found by experiments on the magnet. ”

“ The direction of magnetization of the equivalent magnet may be predicted by remembering that a current travelling round the earth from east to west as the sun appears to do, would be equivalent to that magnetization which the earth actually possesses, and therefore in the reverse direction to that of a magnetic needle when pointing freely. ”

“ The same reasoning as above applied to electric attraction and repulsion may also be applied to forces produced by magnetism, but if we attempt an experimental verification of the general law of forces acting through space we encounter some difficulty. When dealing with electricity it is quite easy to isolate a positive from a negative charge each on its own conductor, or, as we may also term it, it is possible to accumulate free electricity of one sign on a conductor. It is not possible to accumulate only north magnetic matter, or only south magnetic matter on one piece of steel. ”

“ Within the magnet, running through its substance, existed lines of force of the same nature as those without, exactly equal in amount to those without, and were, indeed, continuous with them. The conclusion must logically be that every line of force is a closed circuit.
Having thus established the exact quantitative laws of magneto-electric induction, he then advanced to make use of the induced current as a means of investigating the presence, direction, and amount of magnetic forces—in other words, to explore and measure magnetic fields. ”

“ It is evident, then, that in the case of iron and the magnetic metals, this magnetic influence is such that an expenditure of energy is required, not only to cause these materials to move in rotation so as to cut the lines of the field of the magnetic influence, but also to cause them to move outwards from the seat of the influence along the lines of the field. The movements, indeed, involve transformations of energy totally different in nature. ”

“ To find out what the effect is, we must resort to experiment. Professor Lodge, in his Modern Views of Electricity, shows us the effect of any circulating current of electricity revolving round a magnet. In his [220] chapter on Electro-Magnetism he writes as follows: “How does a current act on a magnetic pole? Two currents attract or repel each other, two poles attract or repel each other, but a current and a pole exert a mutual force which is neither attraction nor repulsion. It is a rotatory force. They tend neither to approach nor to recede, they tend to revolve round each other. ”

“ We have now to consider the magnetization of bodies with respect to the mode in which it may be produced and changed. A bar of iron held parallel to the direction of the earth s magnetic force is found to become magnetic, with its poles turned the opposite way from those of the earth, or the same way as those of a compass needle in stable equilibrium. ”

“ Thus, if a descending current is placed in a field of magnetic force directed towards the north, its magnetic action will be to the north on the west side, and to the south on the east side. Hence the forces strengthen each other on the west side and oppose each other on the east side, and the current will therefore be acted on by a force from west to east. ”

“ Therein he shows, as the result of his customary careful experimental explorations that the magnetism of every known substance (even tissues of the human frame) is manifested in one of two ways. Either the body is, like iron, attracted by the magnet, taking a position coincident with the magnetic forces which he calls paramagnetic (para beside or near, magnetes, magnes, magnet) or bodies—like bismuth, for instance—are repelled by the poles and should therefore be called diamagnetic (dia, across) for they set themselves across, equatorially, or at right angles to the magnetic lines. ”

“ These magnetic storms are attended by brilliant displays of the aurora, and this fact strengthens [Pg 37] the theory that the earth is a great electromagnet; for the stronger the electrical current the more powerful we should expect the magnetism to be, and this is shown by the action of the magnetic needle at such times. The stronger the magnet the more intense will be the lines of force, and naturally the more intense the light, if indeed these lines of force are the cause of the light. ”

“ Let us assume a plain iron core, Fig. 7, magnetized as indicated, so that its poles, N, S, complete their magnetic circuits by what is called free field or lines in space around it. Let a coil of wire be wound thereon as indicated. Now assume that the magnetism is to be lost or cease, either suddenly or slowly. An electric potential will be set up in the coil, and if it has a circuit, work or energy will be produced or given out in that circuit, and in any other inductively related to it. Hence the magnetic field represents work or potential energy. ”

“ Now, although magnetism can not be collected, imprisoned, or discharged, like electricity, or collected at all, but by its adherence to some substance capable of magnetization, it is obvious there is an intimate association, at least, between it and electricity. They are never found alone. All electricity will magnetize. All magnetism will evolve electricity. All currents of electricity have encircling currents of magnetism, and all deflect the magnetic needle. All magnetic currents give out to intersecting wires, currents of electricity, and all magnets induce them. ”

“ But at any intermediate frequency the ascending and descending curves of magnetization will enclose a space, and energy will be dissipated. It is remarkable that the phenomena of magnetic viscosity are much more evident in a thick rod than in a thin wire, or even in a large bundle of thin wires. ”

“ As soon as the magnet is set in action, the discharge, which had before filled the egg, is concentrated into a defined band of light, which rotates steadily round the magnet,—the direction of its rotation being changed by reversal either of the current or of the polarity of the magnet. If we suppose that the aurora is an electric discharge passing from one magnetic pole to the other, and following the terrestrial magnetic curves, we shall find that the theory agrees with observed facts even in its lesser details. ”

“ According to Balfour Stewart, auroræ and earth currents may be regarded as secondary currents resulting from changes in the earth’s magnetism. Magnetic phenomena are included under the general term terrestrial magnetic elements, and consist of magnetic declination, inclination, and intensity.
These are for convenience determined separately; the first by an instrument called a Declinometer, and the second by an Inclinometer or Dipping Needle. ”

“ If therefore a system of currents is excited in a uniform plane sheet of infinite extent and then left to itself, its magnetic effect at any point on the positive side of the sheet will be the same as if the system of currents had been maintained constant in the sheet, and the sheet moved in the direction of a normal from its negative side with the constant velocity . The diminution of the electromagnetic forces, which arises from a decay of the currents in the real case, is accurately represented by the diminution of the force on account of the increasing distance in the imaginary case. ”

“ If is the intensity of magnetization, and A, B, C its components, then, by Art. 400,
We may call these the equations of magnetization, and they indicate that in the electromagnetic system the magnetic induction , considered as a vector, is the sum, in the Hamiltonian sense, of two vectors, the magnetic force , and the magnetization , multi plied by 4 π, or
In certain substances, the magnetization depends on the magnetic force, and this is expressed by the system of equations of induced magnetism given at Arts. ”

“ The currents thus detected are often sufficiently active to deflect a magnetic needle powerfully, to produce, slowly, electro-chemical decomposition, and to render a bar of iron magnetic. These currents must not be confounded with the great electrical movements around the earth. They are only to be detected in those mineral formations in which there is evidence of chemical action going on, and, the greater the amount of this chemical operation, the more energetic are the electrical currents. ”

“ And thus he was enabled, at the end of his second series of ‘Researches’ (December 1831) , to give, in general terms, the law of nature to which may be referred the extraordinary number of new and curious experiments which he has stated (Arts. 256–264) , namely, that if a wire move so as to cut a magnetic curve, a power is called into action which tends to urge a magnetic current through the wire; and that if a mass move so that its parts do not move in the same direction across the magnetic curves, and with the same angular velocity, electrical currents are called into play in the mass. ”

“ In experimenting on magnetic forces we are, therefore, always disturbed by the presence of magnetic matter of the opposite polarity. Another difficulty lies in this, that the magnetic matter is spread over the whole of the bar—more dense at the ends, but still of sensible density at points towards the middle. ”

“ The most obvious mechanical phenomenon in electrical and magnetical experiments is the mutual action by which bodies in certain states set each other in motion while still at a sensible distance from each other. The first step, therefore, in reducing these phenomena into scientific form, is to ascertain the magnitude and direction of the force acting between the bodies, and when it is found that this force depends in a certain way upon the relative position of the bodies and on their electric or magnetic condition, it seems at first sight natural to explain the facts by assuming the existence of something either at rest or in motion in each body, constituting its electric or magnetic state, and capable of acting at a distance according to mathematical laws. ”