366. Magnetic moment. The magnetic moment of a magnet is defined as the product of the strength of one of the poles times the distance between the two poles of the magnet. Or where M is the magnetic moment, m the strength of one of the poles, and I the distance between the poles. Imagine a bar magnet placed at right angles to a field the intensity of which is H (Fig. 224). The force on each pole is mH, according to equation (3). Since these forces are equal but in opposite directions, they form a "couple" (sect. 14) and tend to rotate the magnet. The torque is equal to the product of one of the forces times l, the distance between the poles: Or Torque = mHl N = MH, (5) mH S FIG. 224 since M, the magnetic moment, is equal to ml. It is not very difficult to measure the torque required to hold a magnet perpendicular to a field. If the intensity of the field, H, is known, M can be calculated; or, if M is known, H can be determined. In practically all cases of forces between magnets (complete magnets, not poles) the magnetic moment appears in the algebraic expression for the force or for the torque. It is also true that in nearly all experimental methods of measuring the strength of magnets it is the magnetic moment that is determined. Hence in magnetic measurements magnetic moment is an important quantity. 367. Energy in a magnetic field. It is always true that work must be done to create a magnetic field. There is good evidence for believing that a magnetic field has energy. It can be shown (though the details are beyond the scope of this book) that the energy per cubic centimeter of a magnetic field in air is where H is the strength of the field. (6) 368. Summary. Magnets will attract pieces of iron, nickel, and cobalt, and, very feebly, some other substances. The ends where the attractive force is the greatest are called poles. There are two kinds of poles, northseeking and south-seeking. Each magnet has at least one of each kind. Like poles repel and unlike attract. Magnetic lines are imaginary lines the direction of which gives at any one point the direction of the force in air on a north-seeking pole placed at that point. A short compass needle will always set itself tangentially to a magnetic line. The declination of the earth's magnetic field is measured by the angular deviation of the compass from the north. It is different in different parts of the United States. The inclination, or dip, is the angle the magnetic lines of the earth make with the horizontal. It varies from 65 to 75 degrees in different parts of the United States. The earth's magnetic field is not constant but is gradually changing. In addition to the secular changes, there are daily changes. When a piece of soft iron is brought into a magnetic field, it is mag. netized by induction. The magnetic lines of the field tend to crowd into the iron rather than to go through the air. The attraction of pieces of iron by magnets can be explained by the fact that the pieces of iron become magnetized. Hardened steel does not readily become magnetized, but it retains part of the magnetism when carried out of the field. It is because each particle of iron becomes a complete magnet that iron filings will arrange themselves in lines which in general are in the same direction as the magnetic lines of the field. Iron loses its magnetic properties at a temperature between 700° C. and 800° C. a dull-red heat. All the simple facts of magnetism can be explained by the molecular theory, which assumes that each molecule is a complete magnet. Coulomb's quantitative law of the force acting on each one of two poles in air is, by equation (1), In the C. G. S. electromagnetic system of units the unit for measuring m, the pole strength, is so chosen that k is equal to unity when the poles are separated by air. A C.G.S. unit north-seeking pole, when placed 1 centimeter away from an equal north-seeking pole in air, will repel it with a force of 1 dyne. The force acting on a pole in a field the strength of which is H is, by equation (3), F = Hm. The strength of a magnetic field is equal in both direction and magnitude to the force exerted on a unit north-seeking pole placed in that field. It is customary to make the density, or the number per square centimeter, of magnetic lines in air numerically equal to the strength of the field. This is entirely conventional. The magnetic moment of a bar magnet is the product of the strength of one pole by the distance between the poles, or it is equal to the torque necessary to hold the magnet at right angles to a magnetic field of unit strength. The poles of any magnet always have equal pole strengths. PROBLEMS 1. Find the force of attraction between two poles + 30 and - 20 when placed 10 cm. apart. Find the force when they are 20 cm. apart. ✓ 2. Two equal poles attract each other with a force of 64 dynes when placed 5 cm. apart. Find the strength of one of the poles. ✓ 3. (a) Find the strength of a magnetic field at a point halfway between two poles, + 30 and -20, when the poles are 20 cm. apart. (b) Find the strength of the magnetic field when the second pole is replaced by one of strength + 20. ✓ 4. The poles of a bar magnet are 10 cm. apart. The strength of each pole is 30 C. G.S. units, Compute the strength of the magnetic field at a point 10 cm. from one pole and in the direction of the prolongation of a line joining the two poles. 5. A magnet has a magnetic moment of 600 C.G.S. units. What are the strengths of the poles if they are 20 cm. apart? V 6. A magnet has poles of strength 200 C.G.S. units which are 15 cm. apart. Find the strength of the field at a point 15 cm. from each pole. 7. A pole of strength 20 C.G.S. units is placed in a magnetic field due to another magnet. The force acting on the pole is 70 dynes. Find the strength of the field which is produced at this place by the other magnet. 8. A magnet, magnetic moment 1200 C. G. S. units and length 20 cm., is placed at right angles to the earth's magnetic field. It is found that the force on one of the poles is 36 dynes. What is the strength of the earth's magnetic field? 9. A magnet 20 cm. long, magnetic moment 800 C. G. S. units, is held in a uniform magnetic field at right angles to the direction of the field. The strength of the field is 6 C. G. S. units. Find (a) the force on each pole and (b) the torque acting on the magnet. CHAPTER XXVI ELECTROSTATICS Introduction, 369. Electrified bodies, 370. Two states of electrification, 371. Conductors and nonconductors, 372. Charges of electricity, 373. Fluid theories of electricity, 374. The negative-electron and positive-nucleus theory, 375. The leaf electroscope, 376. Both kinds of electricity produced simultaneously, 377. Electrostatic induction, 378. An explanation of the action of the electroscope, 379. Charging an electroscope by induction, 380. The attraction of pith balls and other bodies explained, 381. The return shock, 382. The electrophorus, 383. Electric charges from dry cells, 384. Electric charges from a power circuit, 385. The distribution of charges on conductors, 386. The action of points, 387. The lightning rod, 388. The law of force between two small electrified spheres, 389. Unit charge, 390. A natural unit of electric charge, 391. The intensity, or strength, of an electric field, 392. Electrical lines: the strain theory, 393. Faraday's icepail experiment, 394. The Leyden jar, 395. A brief history of early electrical discoveries, 396. Summary, 397. ☑ 369. Introduction. It is convenient to discuss the properties of electricity under two heads: electricity at rest (electrostatics) and electricity in motion (electric currents). When electricity is at rest, it has certain properties; when it is in motion, it has certain additional ones. It happens that the most convenient sources of electricity for showing the electrostatic properties are different from those used in getting electric currents. This should not lead the student to believe that he is dealing with different things. 37 370. Electrified bodies. The fact that certain bodies-amber, gums, etc. when rubbed with a cloth acquire the property of attracting light objects has been known a long time, how long we do not know. In the dry weather of deep winter the electrification of fur, wool, silk, and paper is commonly observed. Children learn that sometimes in cold weather they become so electrified by shuffling over a rug or carpet that a vigorous spark occurs when they touch another person. Hard-rubber rods, sealing-wax, celluloid, dry paper, and sulfur, when rubbed with a woolen cloth or on a woolen sleeve, acquire the property of attracting light bodies. Hard-glass tubing when thoroughly dry is also easily electrified. The list is almost endless. Practically every solid, when rubbed with a different substance, acquires this property. Bodies may be electrified by liquids; gasoline, for example, electrifies pipes through which it flows. In dry-cleaning establishments the electrification of woolens and silks when being washed with gasoline is a source of danger, for a small spark may ignite the gasoline. If one is watching for it, one may, in cold, dry weather, find many times a day different objects that have become electrified. When electrified, a body has the property of attracting not only light bodies, such as small pieces of paper, feathers, and pith, but also large bodies. If the larger bodies are free to move so that a small force will move them, this attraction can be easily shown. For example, a horizontal meter stick suspended in a wire stirrup by a thread can easily be made to move by the attraction of an electrified body. Light bodies are commonly used to show this attraction merely because the forces involved are small. The forces produced by electrified bodies are not a special type of force. They obey the same laws of mechanics as all other forces; for example, they obey Newton's laws of motion. Not only will an electrified rod hung in a stirrup attract another object, but the other object (for instance, the hand) will attract it. This is an example of action and reaction. If the rod attracts the hand, the hand must attract the rod. 371. Two states of electrification. If one balances a hard-rubber :rod, which has been electrified by rubbing it with wool, in a stirrup hung by a thread, so that the rod is free to swing around, and then brings near it another similarly electrified rubber rod, he will find that they repel each other. Similarly, a piece of sealing-wax electrified by rubbing it on wool will repel the electrified hard-rubber rod. Further testing will show that while an electrified hardrubber rod repels another hard-rubber rod, a rod of hard glass when rubbed with silk will attract the electrified hard-rubber rod. From this one concludes that there must be more than one state of elec |