14 - Maxwell's theory

Summary

Both empirical considerations and mechanical models of the aether provided the foundation upon which Maxwell built his classical theory of electromagnetism. In this chapter we first discuss some formal aspects of this theory and then turn to observational consequences of it that led to a profound conflict between the principles of classical mechanics and those of electromagnetic theory. This will set the stage for our treatment of relativity in later chapters.

MAXWELL'S EQUATIONS

Prior to Maxwell's great synthesis, the basic laws of the separate fields of electricity and of magnetism were, respectively, Coulomb's law for the electric field E produced by a static point charge q and the Biot–Savart law for the magnetic field B produced by a wire carrying a current i. (See Section 14.A for mathematical statements of these laws and for the mathematical details that support many of the claims made in the present section.) Each of these two laws involves a proportionality constant (say, k₁ and k₂, respectively) that must be determined by experiment. (These are analogous to the constant G in Newton's law of gravitation, Eq. (8.4).) That is, the constants k₁ and k₂ are fixed independently and by different types of phenomena (electrostatics and magnetostatics, respectively). It turns out that the ratio k₁/k₂ has the dimensions of a velocity squared that we denote by c² for reasons that will become evident shortly.