Direct Energy, 2018a

1 INTRODUCTION 15
is likely to be found spatially around an atom. However,identifying the
location of an electron with any degree of precision is dicult for multiple
reasons. First,atoms are tiny,roughly 10 −10 m in diameter. Second,at
any temperature above absolute zero,atoms and electrons are continually
in motion. Third,electrons have both particle-like and wave-like properties.
Fourth,according to Heisenberg's Uncertainty Principle,the position and
momentum of an electron cannot simultaneously be known with complete
precision. At best,you can say that an electron is most likely in some
region and moves with some range of speed. Fifth,in many materials
including conductors and semiconductors,valence electrons are shared by
many atoms instead of bound to an individual atom [10,p. 544].
1.6 Electromagnetic Waves
1.6.1 Maxwell's Equations
In this text, V and I denote DC voltage and current respectively while v
and i denote AC or time varying voltage and current. In circuit analysis,
we are unconcerned with what happens outside these wires. We are only
interested in node voltages and currents through wires. Furthermore,the
voltages and currents in the circuit are described as functions of time t
but not position (x, y, z). Devices like resistors,capacitors,and inductors
too are assumed to be point-like and not extended with respect to position
(x, y, z). This set of assumptions is just a model. In reality,if two nodes in
a circuit have a voltage dierence between them,then necessarily a force
is exerted on nearby charges not in the path of the circuit. This force per
unit charge is the electric eld intensity −→ E . Similarly,if there is current
owing through a wire,there is necessarily a force exerted on electrons in
nearby loops of wire,and this force per unit current element is the magnetic
ux density −→ B . Energy can be stored in an electric or magnetic eld. In
later chapters,we will discuss devices,including antennas,electro-optic
devices,photovoltaic devices,lamps,and lasers,that convert energy of an
electromagnetic eld to or from electricity.
Four interrelated vector quantities are used to describe electromagnetic
elds. These vector elds are functions of position (x, y, z) and time t. The
four vector elds are
−→ E (x, y, z, t)=Electric eld intensity in
V
m
−→ D(x, y, z, t)=Displacement ux density in
C
m 2