33-3 PLANE ELECTROMAGNETIC WAVES AND THE SPEED OF LIGHT
We are now ready to develop the basic ideas of electromagnetic waves and their relation to the principles of electromagnetism as summarized in Maxwell’s equations. Our procedure will be to postulate a simple field configuration that has wavelike behavior. We’ll assume an electric field E that has only a y-component and a magnetic field jj with only a z-component, and we’ll assume that both fields move together in the +x-direction with a speed C that is initially unknown. (As we go along, it will become clear why we choose E and jj to be perpendicular to the direction of propagation as well as to each other.)
Then we will test whether these fields are physically possible by asking whether they are consistent with Maxwell’s equations, particularly Ampere’s law and Faraday’s law. We’ll find that the answer is yes, provided that c has a particular value. We’ll also show that the wave equation, which we encountered during our study of mechanical waves in Chapter 19, can be derived from Maxwell’s equations.