This book has one purpose: to help you understand four of the most influential equations in all of science. If you need a testament to the power of Maxwell's Equations, look around you – radio, television, radar, wireless Internet access, and Bluetooth technology are a few examples of contemporary technology rooted in electromagnetic field theory. Little wonder that the readers of Physics World selected Maxwell's Equations as “the most important equations of all time.”

How is this book different from the dozens of other texts on electricity and magnetism? Most importantly, the focus is exclusively on Maxwell's Equations, which means you won't have to wade through hundreds of pages of related topics to get to the essential concepts. This leaves room for in-depth explanations of the most relevant features, such as the difference between charge-based and induced electric fields, the physical meaning of divergence and curl, and the usefulness of both the integral and differential forms of each equation.

You'll also find the presentation to be very different from that of other books. Each chapter begins with an “expanded view” of one of Maxwell's Equations, in which the meaning of each term is clearly called out. If you've already studied Maxwell's Equations and you're just looking for a quick review, these expanded views may be all you need. But if you're a bit unclear on any aspect of Maxwell's Equations, you'll find a detailed explanation of every symbol (including the mathematical operators) in the sections following each expanded view.

Maxwell's Equations as presented in Chapters 1–4 apply to electric and magnetic fields in matter as well as in free space. However, when you're dealing with fields inside matter, remember the following points:

• The enclosed charge in the integral form of Gauss's law for electric fields (and current density in the differential form) includes ALL charge – bound as well as free.

• The enclosed current in the integral form of the Ampere–Maxwell law (and volume current density in the differential form) includes ALL currents – bound and polarization as well as free.

Since the bound charge may be difficult to determine, in this Appendix you'll find versions of the differential and integral forms of Gauss's law for electric fields that depend only on the free charge. Likewise, you'll find versions of the differential and integral form of the Ampere–Maxwell law that depend only on the free current.

What about Gauss's law for magnetic fields and Faraday's law? Since those laws don't directly involve electric charge or current, there's no need to derive more “matter friendly” versions of them.

The story so far . After the defeat of his generals Datis and Artaphernes at Marathon in 490, Darius intended to invade Greece again, but was distracted by a revolt in Egypt in 486, during which year he died. His son by Atossa, Xerxes, succeeded him and crushed the revolt in 485. Xerxes spent four years preparing his expedition against Greece, the first act being the digging of a canal through the Athos peninsula in 483 (7.22). Late in 481, envoys were sent to demand ‘earth and water’ from the northern Greek states down to Boeotia (46.4n.). The army mustered in Cappadocia, and marched to Sardis, whence in spring 480 it began the expedition; the fleet collected at Abydos (7.20–40). H. gives a total of 5,283,220 men (7.186.2), a fantastic exaggeration no doubt, but indicative of the vast scale of the force. On the way, roads and bridges were constructed, and the Hellespont spanned by pontoons at Abydos (7.33–7). Progress was measured, partly because of the sheer numbers involved, and partly because Xerxes wanted to be able to use the crops in northern Greece to help feed his troops (7.50.4). Army and fleet advanced in contact with each other so as to coordinate their actions (7.236.2), but at the head of the Thermaic gulf in Macedonia, the land route diverged from the coast and they separated, reuniting at Aphetae on the Gulf of Pagasae, where the fleet is waiting at the start of book 8. H. does not tell us enough to be certain which route or (more likely) routes the army took. See map for possible solutions.