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* This is because no sense of direction is involved in nding the sum of di erent amounts of work (energy); for instance, 10 joules 20 joules 30 joules. Electric charge is likewise a scalar quantity.
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CHAPTER 1 Electric Charge and Electric Field
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Thus, if we wish, eld strength can also be expressed in volts per meter, which is dimensionally (that is, in terms of fundamental units) equal to newtons per coulomb. Problem 3 The product qV is in what units Problem 4 What is the potential di erence between two points if 2.65 joules of work is done in moving 0.0078 coulombs of charge between the two points Problem 5 " " Let Ea and Eb denote the eld strength at two di erent points, a and b, in an electric " " eld. If the values of Ea and Eb are given, would this information alone be su cient to allow the calculation of the potential di erence V between the two points
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Electric Current. Ohm s Law. Basic Circuit Configurations
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2.1 Electric Current
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Electric charge in motion is called electric current ; that is, ELECTRIC CURRENT is simply ELECTRIC CHARGE IN MOTION. The concept of electric current is important because it is through the medium of electric current that practical use is made of the phenomenon of electricity. Let us look again at Figs. 5 and 6 in Chap. 1. In Fig. 6, when the switch is closed the excess charge which ows to the earth through the copper wire constitutes an electric charge owing in the wire. This electric current continues to ow until body A becomes electrically neutral, at which time the current ceases. Electric current is measured in terms of the RATE OF FLOW of electric charge; thus, since charge is measured in coulombs and time is measured in seconds, we have the de nition Electric current is measured in coulombs per second which is given the special name amperes. Electric current is represented by the letter i. i current in AMPERES COULOMBS PER SECOND ` The ampere, named in honor of the French physicist Ampere, is pronounced AM peer in English-speaking countries. Let us now consider a cross section of a copper wire, or other conductor, through which electric current is owing, as in Fig. 15. Let the current be owing from left to right, as suggested by the lines with the arrowheads.
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CHAPTER 2 Electric Current. Ohm s Law
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Fig. 15
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If the wire in Fig. 15 is carrying a current of one ampere it means that electric charge is owing across the area A at the rate of one coulomb per second. That is, one coulomb of charge passes through the area A every second. Actually, the above statement is basically for the case where a STEADY, constant current of 1 ampere is owing in the wire. If the current is not steady, but changes with time, that is, changes from instant to instant, then we must use the delta notation, thus, q i t 9
In the above, q denotes a small amount of charge that passes through area A in a small interval of time t. Thus eq. (9) gives the average current over an interval of time t; the smaller t is, the smaller is q, and the closer eq. (9) comes to being instantaneous or exact current at a time t.* Let us now continue, with a discussion of some details concerning electric charge and current. Imagine that you are viewing a large cone-shaped pile of sand from a distance of say several hundred feet. Viewed from such a distance, the pile of sand appears to be a continuous substance, because you are not close enough to see the individual grains or particles that sand is actually made of. Of course, as you approach the pile, and come right up to it, you begin to see that sand is not a continuous substance, but is actually composed of discrete (separate) particles or grains. The same principle of graininess applies to all matter, be it gaseous, liquid, or solid, except that the grains are extremely small particles called atoms and molecules. For instance, the water we see in a cup is not a continuous substance, but is composed of a vast number of tiny molecules of water. A single molecule of water is far too small to be seen under the most powerful microscope, but their existence has been proved by indirect means. We know that a single drop of water is composed of billions upon billions of individual water molecules. Water, as you know, is a compound of hydrogen and oxygen, each molecule of water being composed of two atoms of hydrogen and one atom of oxygen, the atoms being bound together by electrostatic forces. All atoms and molecules are themselves composed of electrons, protons, and neutrons, as follows. Electrons are tiny, basic units of negative electric charge; ALL electrons carry the same amount of negative charge which is often denoted by e where, approximately, e 1:602 10 19 coulomb of negative charge Protons are the tiny, basic units of positive electric charge; ALL protons carry the same amount of positive charge, which has the same magnitude as that of the electron but of opposite sign. The proton, however, has considerably more mass than the electron, the mass of the proton being about 1845 times that of the electron.