Most students in engineering and science have heard the term “Maxwell’s equations,” and some may also have heard that
Maxwell’s equations “describe all electromagnetic phenomena.” However, it is not always clear what exactly do we mean by
these equations. How are they any different from what we have studied in the previous chapters? We recall discussing static
and time-dependent fields and, in the process, discussed many applications. To do so, we used the definitions of the curl and
divergence of the electric and magnetic fields: what we called “the postulates.” Are Maxwell’s equations different? Do they
add anything to the previously described phenomena? Perhaps the best question to ask is the following: Is there any other
electromagnetic phenomenon that was not discussed in the previous chapters because the definitions we used were not
sufficient to do so? If so, do Maxwell’s equations define these yet unknown properties of the electromagnetic field? The
answer to the latter is emphatically yes.
In fact, we do not need to go far to find applications which could not be treated using, for example, Faraday’s law. The
most obvious is transmission of power as, for example, in radio or television. All applications related to transmission of
power (radar, communication, radio, etc.) were conspicuously missing in the previous chapters, but there is an even more
important (and related) aspect of the electromagnetic field which was not mentioned until now. Take, for example, induction
of voltage in a loop. Faraday’s law gives an accurate statement of how the induction occurs and the magnitude of the induced
emf. Now let’s say that two loops are located a short distance from each other and one loop induces an electromotive force in
the second. If we were to separate the loops a very long distance from each other and measure the induced voltage in the
second loop, the magnitude will be very small. The question is, however, this: Is there any lag in time between switching on
the current in the first loop and detection of the induced voltage in the second loop because of the distance between the
loops? Faraday’s law says nothing about that and neither do any of the postulates used previously. Intuitively, we know there
must be a time lag since nothing can occur instantaneously. In this regard, consider the following: On January 22, 2003,
NASA received the last transmission from the Pioneer 10 space probe. At that time, Pioneer 10 was 5 weeks shy of its 31st
year of space flight and was over 12.2 billion km from the Earth.1 At that distance, the transmission took approximately 11 h
18 min to reach the Earth. This is hardly instantaneous. In fact, if we divide distance by time, we find that the information has