A medium with electromagnetic properties modifies an electromagnetic field imposed on it. The response of some media may be described satisfactorily in terms of induced dipole moments, and this is particularly the case for the response to static fields. The response to a fluctuating field may also be described in terms of the induced current density. This alternative description is used widely in plasma physics and is emphasized in the approach adopted here.

In Part Two the nature of electromagnetic responses is discussed in Chapter 6 and general properties of response tensors are summarized in Chapter 7. An understanding of the material in these two chapters is important in the discussion of waves in media in Part Three. The remaining three Chapters in Part Two are more of the nature of reference material. Although much of the material in these Chapters is referred to and used in the remainder of the book, a detailed understanding of this material is not essential before proceeding to Parts Three, Four and Five.

The formal theory of waves is developed by solving the wave equation. The condition for a solution to exist leads to a dispersion equation, and each specific solution of this equation is called the dispersion relation for a particular wave mode. An arbitrary wave mode is referred to as “the mode M”. The polarization vector for the mode M is defined as a unimodular vector along the direction of the electric vector found by solving the wave equation for waves in the mode M. Specific examples of wave modes are discussed for isotropic media, anisotropic crystals and cold magnetized plasmas. Transverse waves in a isotropic medium correspond to two degenerate wave modes, and the description of their polarization is discussed separately.

The first sustained nuclear chain reaction was achieved by Enrico Fermi and his collaborators at the University of Chicago on December 2, 1942. Since then, nuclear energy has been one of the dominant factors in our society. Fission reactors are widely used to supplement the generation of electric power and, when it is realized, controlled thermonuclear fusion promises to be an inexhaustible source of energy for mankind. Yet the most decisive and terrifying aspect of nuclear energy so far has been in the production of weapons of unprecedented destructive power. These weapons if used in the large quantities presently available can alter the ecology of the planet and completely destroy, or at the least, radically change human and animal life from what we know it to be today.

In Chapter 5 we begin by discussing the units of energy, the various levels of energy consumption and supply, and the global balance of energy on the earth. The earth receives its energy from the sun, which generates energy by nuclear fusion. Next we review the facts associated with nuclear forces in order to discuss the release of energy in fission and fusion processes. We also discuss radioactivity, its detection and its effect on living organisms. One section is devoted to nuclear reactors and another section to the principles of controlled nuclear fusion. For completeness we also consider solar energy, which even though still economically impractical is an inexhaustible source of clean energy.

Transportation, of people and materials, is among the major factors that have made our civilization possible. The harnessing of animals and the use of ships were exploited early in the history of man. The sailing boat was an extraordinary invention because the sea offered reduced friction to the point where the wind would suffice to propel the ship. Railroads provided the freight capacity that made possible the industrial revolution, to be followed by the introduction of the automobile in the 20th century. The first airplane flight by the Wright brothers took place in 1903, and today transportation has brought within easy access all parts of the globe. This speed and ease in transportation has had and continues to have a profound effect in shaping the social and economic structure of the world community. In 1969 man landed on the moon, and unmanned spacecraft have reached to the edge of our planetary system. More ambitious missions into space can be foreseen as technology advances and the desire to carry them out persists.

Chapter 7 is devoted to a discussion of airplane and rocket flight and propulsion. In contrast to ships which are buoyant, airplanes are heavier than air and are supported by the dynamically produced lift. The reduced friction in air allows airplanes to reach high velocities, even in excess of the speed of sound. While airplanes must fly in the atmosphere, rockets are not subject to such a restriction.

Modern electronic devices operate in general, on digital principles. That is, signals are transmitted in numerical form such that the numbers are coded by binary digits. A binary digit has only two states: ‘one’ and ‘zero’, or ‘high’ and ‘low’ etc. The reason for relying almost exclusively on digital information is that binary data can be easily manipulated and can be reliably stored and retrieved. That this approach is practical and economically advantageous is due to the great advances in large scale integration and chip manufacture as already discussed. In this chapter we will consider digital systems and the representation and storage of binary data. We will conclude by discussing the architecture of a small 3-bit computer, which nevertheless, contains all the important features of large machines.

Elements of Boolean algebra

In digital logic circuits a variable can take only one of the two possible values: 1 or 0. The rules for operating with such variables were first discussed by the British mathematician George Boole (1815–64) and are now referred to by his name. Since in pure logic a statement is either true or false, Boolean algebra can be applied when manipulating logic statements as well. This material is conceptually simple yet it is most relevant to the understanding of complex logic circuits.

Boolean algebra contains three basic operations: AND, OR and Complement. The result of these operations can be best represented by a truth table as introduced in Section 1.9, where also the symbols for the corresponding circuits were given.

Fluid flow and dynamic lift

The motion of a fluid is extremely complex because the individual molecules are subject to random thermal motion as well as to the collective motion of the fluid as a whole. Thus we consider a small element dτ of the fluid and follow its motion as a function of time. We will assume that the fluid is incompressible, so that the mass dm = ρ dτ contained in the volume dτ remains fixed and the density ρ is constant throughout the fluid; we will also assume that the fluid is non-viscous, that is there are no internal frictional forces. These two assumptions are applicable to motion through air when the velocity v is small as compared to the velocity of sound vs, i.e. v « vs. The velocity of sound is a measure of the random thermal velocity of the molecules; its value for air at s.t.p. is vs ≃ 330 m/s. When necessary we will relax these assumptions.

The simplest form of flow occurs when the velocity at each point of the liquid remains constant in time. This is illustrated in Fig. 7.1(a) where the element dτ follows the path from the point P to Q to R and has the velocity vP, vQ, vR; at a later time another element of the fluid will be at P but it will again follow the path to Q to R and have the same velocity.