Page 23 - Maxwell House

BASIC EQUATIONS OF MACROSCOPIC ELECTRODYNAMICS 3

Introduction

There are two basic versions of Maxwell’s equations: microscopic or quantum form and
macroscopic or classical form. The first set is more fundamental and describes the microscopic
fields while taking into account their quantum nature. The second set is more straightforward
and fun because it averages all charges and fields in macroscopic media and allows us to ignore
the quantum effects while giving us sophisticated enough and closed to reality picture of
surrounding world. Maxwell’s equations are essential not only for understanding the world
around us but strikingly successful in explaining and predicting a broad range of
electromagnetic phenomena. Macroscopic Electrodynamics deals with fields averaged on a
spatial and temporal scale that is quite large compared to the interatomic space (in average
10 −10 m) and the time of atomic fluctuations (in average 10 −11 s).
The scale of both values is negligible from engineer’s perspective. In 2014, the Intel
Corporation start mass production of new chips using very sophisticated the 14 nm technology
enabling the manufacture of monolithic integrated circuits (IC) with conductive line widths of a
few tens of nanometers (close to 10 m ). Even this tiny width is two orders of magnitude
−8
higher than the average space between atoms. It means that, so far, the successful IC circuitry
analysis stays in the range of classic electrodynamics settings. Note that the next just coming
step is the 10 nm process.

1.1 MACROSCOPIC ELECTRODYNAMICS

1.1.1 Duality of Electromagnetic Waves

We know from quantum physics about electromagnetic wave duality. They are both waves and
discrete particles, photons. Each photon carries a portion of energy = ℎ, where ℎ =
−34
6.6260755 ∙ 10 [J∙s] is Planck’s constant and is the electromagnetic field frequency. Even
at ultra-high frequency of 1 THz (1,000,000,000,000 Hertz) a single photon carries just
6.6260755 ∙ 10 −22 Joules, an extremely small amount in macroscopic world. For comparison,

Figure 1.1.1 Electromagnetic spectrum