PROBLEMS 1. Find the force between two charges, +80 and 20, placed 20 cm. apart. What is the force when they are 40 cm. apart? 2. Find the intensity of the electric field at a point halfway between two charges, + 40 and - 20 electrostatic units, placed 20 cm. apart. 3. Find the intensity of the electric field at a point halfway between two charges, + 40 and + 40 electrostatic units, placed 20 cm. apart. 4. The force acting on a charge of + 20 electrostatic units, when brought to a certain place in an electric field, was 40 dynes. What was the intensity of the electric field at that place? 5. Two charges, of + 90 and - 40 electrostatic units, are placed 30 cm. apart. What is the intensity of the electric field (a) at a point on the extension of the line joining them, 20 cm. from the negative charge and 50 cm. from the positive? (b) at a point on the other side, 20 cm. beyond the positive charge ? 6. Two charges, of + 40 and - 40 electrostatic units, are 10 cm. apart. (a) What is the intensity of the electric field at a point 10 cm. from each charge? (b) If a charge of + 5 electrostatic units is placed at this point, what will be the magnitude of the force acting on it? 7. A charge of + 25 electrostatic units is carried into a room on an insulated conductor. What will be the total induced charge on the walls and objects in the room? CHAPTER XXVII SIMPLE PROPERTIES OF ELECTRIC CURRENTS The voltaic cell, 398. Unit for measuring current, 399. Resistance, 400. The electromotive force of a cell, 401. Effects of electric currents, 402. Heating effects, 403. Chemical, or electrolytic, effects, 404. Magnetic effects, 405. Mechanical force acting on a wire carrying current in a magnetic field, 406. This chapter contains only a brief description of the more commonly known effects of electric currents (electricity in motion). The purpose is to give the student a general view of some of the facts and a knowledge of some of the terms used in practical work. 398. The voltaic cell. Most of us know that the common dry cell will give an electric current. For example, when a small incandescent lamp is connected to a dry cell by means of metallic wires, the existence of a current is shown by the heating of the lamp filament to incandescence. In order to light this lamp by a cell two things are necessary: 1. The lamp must be connected to the cell by good conductors of electric currents. Copper wire is commonly used. In ability to conduct electricity silver ranks first, with copper next. Nonmetallic substances are poor conductors and usually will not carry enough current to light the lamp. 2. The electric circuit must be closed. A metallic conductor must connect one terminal of the cell to one terminal of the lamp, and another conductor must connect the other lamp terminal to the other terminal of the cell. If the circuit is open at any point, even if the gap is only a microscopic one, the current will not flow. There must be a complete path from one terminal of the cell, through the lamp, back to the other cell terminal. The switch for our electric lights, or the push button of our doorbells, is a device by which the circuit is opened or closed at will. The ordinary dry cell is only one type of voltaic cell. There are many other types of cells in more or less common use. The gravity cell, which contains two solutions, one of zinc sulfate and the other of blue vitriol (copper sulfate), is often used in telegraph circuits. The name voltaic is applied to all these cells, because Volta, in 1799, was the first to construct a cell that would produce an electric current. 399. Unit for measuring current. The current which flows from a voltaic cell or from any other source is usually measured in amperes. For example, ordinary incandescent lamps used in houselighting have from a fourth of an ampere to one ampere of current flowing through them. 400. Resistance. If, instead of copper wires, iron wires of the same size and length are used to connect a lamp to a dry cell, the lamp will not glow so brightly, thus showing that there is less current in the circuit. We say that iron wires have a greater resistance than copper wires of the same diameter. When a cell is connected through any closed circuit, the current which the cell produces depends on how much electrical resistance there is in the entire circuit. Long wires have greater resistance than short ones of the same diameter; hence a cell cannot give so large a current through long wires as when short ones are used. An analogous case is a water pump connected to a pipe line which runs out and then back to the pump. The pump can keep the water circulating in this pipe, but the amount of current which flows through the pipe will depend, in part at least, on the resistance offered by the pipe. The longer the pipe or the smaller the diameter, the less the current that will be produced. So it is with the cell: when longer wires, or smaller ones, or those made of a poorer conducting material are used, less current will travel around the circuit. Resistance is usually measured in ohms! 401. The electromotive force of a cell. The current from a cell or battery depends on two things: (1) the resistance of the circuit and (2) the electromotive force (or E.M.F.) of the cell or battery. The electromotive force is commonly measured in volts; for example, that of a dry cell is about 1.5 volts. When two dry cells are connected in series (that is, the carbon of one connected to the zinc of the other), the electromotive force of the combination is the sum of the two, or about 3 volts. Such a group of cells is called a battery. Batteries for flash lights usually consist of two or three dry cells connected in series. The current in a circuit is directly proportional to the electromotive force and inversely proportional to the resistance of the circuit. Or the number of amperes is directly proportional to the number of volts and inversely proportional to the number of ohms of the complete circuit. This rule, commonly called Ohm's law, will be discussed more fully in a later chapter. 402. Effects of electric currents. The more commonly known effects of electric currents can be grouped under the following heads: 1. Heating (and, as a result, lighting) effects. 2. Chemical or electrolytic effects. 3. Magnetic effects (as in electric bells and telegraph sounders). 4. Mechanical force acting on wires carrying currents in them (as in an electric fan or in the starter of an automobile which is run by such force). These will be explained briefly, in order. The student should note carefully that these effects are due to what is called an electric current, to electricity in motion. 403. Heating effects. The heating of a lamp filament by the current flowing through it has already been mentioned. In the case of an electric iron or an electric stove the current flowing through coils of wire develops heat in them, often making them red-hot. The precise laws which state the amount of heat developed will be given later. One point should be noted here: for the same amount of current a good conductor is heated less than a poor one. When the same current flows through a copper wire and an iron wire of the same size, greater heat is developed in the iron wire. It is for this reason that the heating-coils of electric irons, stoves, etc. are made of relatively poor conductors. For the same current the rate of development of heat is proportional to the resistance of the conductor. 404. Chemical, or electrolytic, effects. If two plates of copper are placed in a solution of blue vitriol (copper sulfate) and connected to several dry cells so that a current flows through the solution from one plate to the other, copper will be deposited on one plate and dissolved from the other. If, instead of the copper plate on which the deposit forms, a plate of some other metal is used, copper will be deposited on it. This process is known as electroplating. Gold, silver, and nickel are also readily deposited by an electric current when the proper liquid is used. All the common nickel-plated objects are plated by means of an electric current. Gold-plating and silver-plating, in nearly all cases, are done by the electrical process. The chemical action of currents was one of the first effects of an electric current to be discovered. In March, 1800, Volta sent a letter to England in which he described the voltaic cell. Within a few weeks Sir Anthony Carlisle and William Nicholson found that water could be decomposed into hydrogen and oxygen. Soon after that, Ritter, of Silesia, found that when a current passed through a solution of blue vitriol one of the wires dipping into the solution was copper-plated. The subject of electrolytic effects is so important that an entire chapter (XXXI) will be devoted to it. 405. Magnetic effects. Although something was known about magnetism and electricity more than a thousand years ago, no relation or connection between them was discovered until the nineteenth century. There are two fundamental relationships between magnetism and electricity, both of tremendous importance. One of these will be described here; the student should be on the lookout for the other. In 1819 the Danish physicist Hans Christian Oersted found that when a wire carrying a current was held over a compass needle, the needle was deflected, tending to set itself at right angles to the wire. This now ranks as one of the two or three most important discoveries in electricity. One way of describing this discovery is to say that Oersted found that a current flowing in a wire produced a magnetic field; for he found that when a magnet (compass needle) was brought near a wire, forces acted on the poles of the magnet, and this is the test for the existence of a magnetic field. The reason that this discovery ranks so high is that most |