Flashes of lightning over a mile long have often been observed (see opposite page 258). Thunder is due to the violent expansion of heated air along the path of discharge. The roll of thunder is due to reflections of the sound from clouds, hills, etc.* SUMMARY. An electrical charge resides on the outside of a conductor because of the mutual repulsion of the like parts of the charge. The electrical density of a charge is greatest on sharp curves; on points, it is so great that the adjacent air becomes ionized. The discharging effect of points is due to the conducting power of ionized air in the vicinity of the point. Lightning rods owe their usefulness to the discharging effects of their points. QUESTIONS AND PROBLEMS 1. Will a solid sphere hold a larger charge of electricity than a hollow one of the same diameter ? 2. Represent by a drawing the electrical condition of a tower just before it is struck by lightning, assuming the cloud at this particular time to be powerfully charged with + electricity. 3. When a negatively electrified cloud passes over a house provided with a lightning rod, the charged points ionize the air, and the charged cloud is thereby rendered less dangerous. Explain. POTENTIAL AND CAPACITY 293. Potential difference. There is a very instructive analogy between the use of the word "potential" in electricity and "pressure" in hydrostatics. For example, if water will flow from tank A to tank B through the connecting pipe R (Fig. 236), we infer that the hydrostatic pressure at a must be greater than that at b, and we attribute the flow directly to this difference in pressure. In exactly the same way, if, when two bodies A and B (Fig. 237) are connected by a conducting wire r, a charge of electricity is found to pass * A laboratory exercise on static electrical effects should follow the discussion of this section. See, for example, Experiment 33 of "Exercises in Laboratory Physics," by Millikan, Gale, and Davis. from A to B (that is, if electrons are found to pass from B to A), we say that the electrical potential is higher at A than at B, and we assign this difference of potential as the cause of the flow. Thus, just as water tends to flow from points of higher hydrostatic pressure to points of lower hydrostatic pressure, so electricity tends to flow from points of higher electrical pressure, or potential, to points of lower electrical pressure, or potential. R B Again, if water is not continuously FIG. 236. Illustrating supplied to one of the tanks A or B hydrostatic pressure of Fig. 236, we know that the pressures at a and b must soon become the same. Similarly, if no electricity is supplied to the bodies A and B of Fig. 237, their potentials very quickly become the same. In other words, all points on a system of connected conductors in which the electricity is in a stationary, or static, condition are at the same potential. This result follows at once from the fact of mobility of electrical charges through conductors. A B FIG. 237. Illustrating electrical pressure But if water is continuously poured into A and removed from B (Fig. 236), the pressure at a will remain permanently above the pressure at b, and a continuous flow of water will take place through R. So, if A (Fig. 237) is connected with an electrical machine and B to earth, a permanent potential difference will exist between A and B, and a continuous current of electricity will flow through r. Difference in potential is commonly denoted simply by the letters P.D. (Potential Difference). * Franklin thought that it was the positive electricity which moved through a conductor, and he conceived the negative as inseparably associated with the atoms. Hence it became a universally recognized convention to regard electricity as moving through a conductor in the direction in which a + charge would have to move in order to produce the observed effect. It is not desirable to attempt to change this convention now, even though the electron theory has exactly inverted the rôles of the + and - charges. 294. Some methods of measuring potentials. The simplest and most direct way of measuring the potential difference between two bodies is to connect one to the knob, the other to the conducting case,* of an electroscope. The amount of separation of the gold leaves is a measure of the P.D. between the bodies. The unit in which P.D. is usually expressed is called the volt. It will be accurately defined in § 335. It will be sufficient here to say that it is approximately equal to the electrical pressure between the ends of copper and zinc strips when dipped in dilute sulphuric acid or to two thirds of the electrical pressure between the zinc and carbon terminals of the familiar dry cell. FIG. 238. Electrostatic voltmeter Since the earth is, on the whole, a good conductor, its potential is everywhere the same (§ 293); hence it makes a convenient standard of reference in potential measurements. To find the potential of a body relative to that of the earth, we connect the outer case of the electroscope to the earth by means of a wire and connect the body to the knob. If the electroscope is calibrated in volts, its reading gives the P.D. between the body and the earth. Such calibrated electroscopes are called electrostatic voltmeters. They are the simplest and in many respects the most satisfactory forms of voltmeters to be had. Their use, both in laboratories and in electrical-power plants, is rapidly increasing. They can be made to measure a P.D. as small as rooo volt and as large as *If the case is of glass, it should always be made conducting by pasting tinfoil strips on the inside of the jar opposite the leaves and extending these strips over the edge of the jar and down on the outside to the conducting support on which the electroscope rests. The object of this is to maintain the walls always at the potential of the earth. 200,000 volts. Fig. 238 shows one of the simpler forms. The outer case is of metal and is connected to earth at the point a. The body whose potential is sought is connected to the knob b. This is in metallic contact with the light aluminum vane c, which takes the place of the gold leaf. A very convenient way of measuring a large P.D. without a voltmeter is to measure the length of the spark that will pass between the two bodies whose P.D. is sought. The P.D. is roughly proportional to spark length, each centimeter of spark length representing a P.D. of about 30,000 volts if the electrodes are large compared to their distance apart. 295. Condensers. Let a metal plate A be mounted on an insulating base and connected with an electroscope, as in Fig. 239. Let a second plate B be similarly mounted and connected to earth by a conducting A B wire. Let A be charged and the deflection of the gold leaves noted. If now we push B toward A, we observe that, as it comes near, the leaves begin to fall together, showing that the potential of A is diminished by the presence of B, although the quantity of electricity on A has remained unchanged. If we convey additional - charges to A with the aid of a proof plane, we shall find that many times the original amount of electricity may now be put on A before the leaves return to their original divergence; that is, before the body regains its original potential. FIG. 239. The principle of the condenser We say, therefore, that the capacity of A for holding electricity has been very greatly increased by bringing near it another conductor connected to earth. It is evident from this statement that we measure the capacity of a body by the amount of electricity which must be put upon it to raise the potential a given amount. The explanation of the increase in capacity in this case is obvious. As soon as B was brought near to A |