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Chapter 2: Introduction to Electrodynamics Maxwell s differential equations in the time domain Whereas the Lorentz force law characterizes the observable effects of electric and magnetic fields on charges, Maxwell s equations characterize the origins of those fields and their relationships to each other. The simplest representation of Maxwell s equations is in differential form, which leads directly to waves; the alternate integral form is presented in Section The differential form uses the vector del operator : x + y +z ( ) x y z where x , y , and z are defined as unit vectors in cartesian coordinates. Relations involving are summarized in Appendix D. Here we use the conventional vector dot product1 and cross product2 of with the electric and magnetic field vectors where, for example: E = x Ex + y Ey +z Ez ( ) E E E x y E + + z ( ) x y z We call E the divergence of E because it is a measure of the degree to which the vector field E diverges or flows outward from any position.

where the arbitrary function Ex(z - ct) might be that illustrated in Figure 2.2.1 at time t = 0 and again at some later time t. Note that as time advances within the argument (z - ct), z must advance with ct in order for that argument, or⎯E at any point of interest on the waveform, to remain constant. Ex(z,t) ⎯z t = 0 t > 0 z = ct

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