232. Medical Applications.—Electric currents have been successfully employed as an adjunct in restoring persons rescued from drowning; the contraction of the diaphragm and chest muscles serving to start respiration. Since the discovery of the Leyden jar many attempts have been made to establish an electrical medical treatment. Discontinuous currents, particularly those furnished by small induction-coils and magnetoelectric machines, are employed by practitioners to stimulate the nerves in paralysis and other affections. Electric currents should not be used at all except with great care, and under the direction of regularly trained surgeons.1 1 It is not out of place to enter an earnest caution on this head against the numerous quack doctors who deceive the unwary with magnetic and galvanic "appliances." In many cases these much-advertised shams have done incalculable harm: in the very few cases where some fancied good has accrued the curative agent is probably not magnetism, but flannel! Part Second. CHAPTER IV. ELECTROSTATICS. LESSON XX.-Theory of Potential. 233. By the Lessons in Chapter I. the student will have obtained some elementary notions upon the existence and measurement of definite quantities of electricity. In the present Lesson, which is both one of the hardest and one of the most important to the beginner, and which he must therefore study the more carefully, the laws which concern the magnitude of electrical quantities and their measurement are more fully explained. In no branch of knowledge is it more true than in electricity, that "science is measurement." That part of the science of electricity which deals with the measurement of charges of electricity is called Electrostatics. We shall begin by discussing first the simple laws of electric force, which were brought to light in Chapter I. by simple experimental means. 234. First Law of Electrostatics. -Electric charges of similar sign repel one another, but electric charges of opposite signs attract one another. The fundamental facts expressed in this Law were fully explained in Lesson I. Though familiar to the student, and apparently simple, these facts require for their complete explanation the aid of advanced mathematical analysis. They will here be treated as simple facts of observation. 235. Second Law of Electrostatics.-The force exerted between two charges of electricity (supposing them to be collected at points or on two small spheres), is directly proportional to their product, and inversely proportional to the square of the distance between them. This law, discovered by Coulomb, and called Coulomb's Law, was briefly alluded to (on page 16) in the account of experiments made with the torsion-balance; and examples were there given in illustration of both parts of the law. We saw, too, that a similar law held good for the forces exerted between two magnet poles. Coulomb applied also the method of oscillations to verify the indications of the torsion-balance and found the results entirely confirmed. We may express the two clauses of Coulomb's law, in the following symbolic manner. Let fstand for the force, q for the quantity of electricity in one of the two charges, and q' for that of the other charge, and let d stand for the distance between them. Then, and (1.) ƒ is proportional to q × q', (2.) fis proportional to I d2 These two expressions may be combined into one; and it is most convenient so to choose our units or standards of measurement that we may write our symbols as an equation :— f = 9x q 236. Unit of Electric Quantity.-If we are, however, to write this as an equality, it is clear that we must choose our unit of electricity in accordance with the units already fixed for measuring force and distance. All electricians are now virtually agreed in adopting a system which is based upon three fundamental units: viz., the Centimetre for a unit of length; the Gramme for a unit of mass; the Second for a unit of time. All other units can be derived from these, as is explained in the Note at the end of this Lesson. Now, amongst the derived units of this system is the unit of force, named the Dyne, which is that force which, acting for one second on a mass of one gramme, imparts to it a velocity of one centimetre per second. Taking the dyne then as the unit of force, and the centimetre as the unit of length (or distance), we must find a unit of electric quantity to agree with these in our equation. It is quite clear that if q, q', and d were each made equal to I (that is, if we took two charges of value I each, and placed them one centimetre apart), the value of 9 × q would be ,which is equal to I. Hence we d2 adopt, as our Definition of a Unit of Electricity, the following, which we briefly gave at the end of Lesson II. One Unit of Electricity is that quantity which, when placed at a distance of one centimetre (in air) from a similar and equal quantity, repels it with a force of one dyne. IX I An example will aid the student to understand the application of Coulomb's law. EXAMPLE. Two small spheres, charged respectively with 6 x 8 42 48 16 d2 = = 3 dynes. Examples for the student are given in the Questions at the end of the Book. The force in the above example would clearly be a force of repulsion. Had one of these charges been negative, the product q× q' would have had a value, and the answer would have come out as minus 3 dynes. The presence of the negative sign, therefore, prefixed to a force, will indicate that it is a force of attraction, whilst the sign would signify a force of repulsion. 237. Potential. -We must next define the term potential, as applied to electric forces; but to make the meaning plain a little preliminary explanation is necessary. Suppose we had a charge of + electricity on a small insulated sphere A (See Fig. 95), placed by itself and far removed from all other electrical charges and electrical conductors. If we were to bring another body B near it, charged also with + electricity, A would repel B. But the repelling force would depend on the quantity of the new charge, and on the distance at which it was placed. Suppose the new charge thus brought near to be one unit of + electricity; when B was a long way off it would be repelled with a very slight force, and very little work need be expended in bringing it up nearer against the repelling forces exerted by A; but as B was brought nearer and nearer to A, the repelling force would grow greater and greater, and more and more work would have to be done against these opposing forces in bringing up B. Suppose that we had begun at an infinite distance away, and that we pushed up our little test charge B from B' to B" and then to Q, and so finally moved it up to the point P, against the opposing forces exerted by A, we should have had to spend a certain amount of work; that work represents the potential' at the point P due to A. For the following is the definition of electrostatic potential :— The potential at any point is the work that must be spent 1 In its widest meaning the term "potential" must be understood as "power to do work." For if we have to do a certain quantity of work against the repelling force of a charge in bringing up a unit of electricity from an infinite distance, just so much work has the charge power to do, for it will spend an exactly equal amount of work in pushing the unit of electricity back to an infinite distance. If we lift a pound five feet high against the force of gravity, the weight of the pound can in turn do five foot-pounds of work in falling back to the ground. See the Lesson on Energy in Professor Balfour Stewart's Lessons in Elementary Physics. |