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3) Radiation
A stationary charge has a constant 𝐸-field, no 𝐵-field, and
hence produces no radiation.
A uniformly moving charge has both 𝐸&𝐵-fields but it
does not radiate.
If a charge moves no uniformly, it radiates.

3-1)Electric Dipole Radiation

Perhaps the simplest electromagnetic wave-producing
mechanism to visualize is the oscillating dipole – two
opposite charges, vibrating to and fro along a straight
line. Any yet this arrangement is surely the most
important at all. Both light and UV radiation arise primary
from the rearrangement of the outermost, or weakly
bound, electrons in atoms and molecules. It follows from
the quantum-mechanical analysis that the electric dipole
moment of the atom is the major source of this radiation.

The fig. above schematically depicts the electric field distribution in the region of an electric dipole. In this configuration, a
negative charge oscillates linearly in simple harmonic motion about an equal stationary positive charge. If the angular
frequency of the oscillation is w, the time-dependent dipole moment 𝑝(𝑡) has the scalar form 𝑝 = 𝑝0 𝑐𝑜𝑠𝑤𝑡. Note that
𝑝(𝑡 ) could represent the collective moment of the oscillating charge distribution on the atomic scale or even an oscillating
current in a linear television antenna.
At t = 0,𝑝 = 𝑝0 = 𝑞𝑑, where d is the initial maximum separation between the centers of the two charges (The fig. above,
a). The dipole moment is actually a vector in the direction from -q to +q. The figure shows a sequence of field line patterns
as the displacement, and therefore the dipole moment decreases, then goes to zero, and finally reverses direction. When
the charges effectively overlap,𝑝 = 0, and the field lines must close on themselves.
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Very near the atom, the 𝐸-field has the form of a static electric dipole. A bit farther out, in the region where the closed
loops form, there is no specific wavelength. The detailed treatment shows that the electric field is composed of five
different terms, and things are fairly complicated. Far from the dipole, in what is called the wave or radiation zone, the field
configuration is much simpler. In this zone, a fixed wavelength has been established; 𝐸 and 𝐵 are transverse, mutually
perpendicular, and in phase.

3-2) The emission of light from atoms

Surely the most significant mechanism responsible for the natural emission and absorption of radiant energy especially
of light—is the bound charge, electrons confined within atoms. These minute negative particles, which surround the
massive positive nucleus of each atom, constitute a kind of distant, tenuous charged cloud. Much of the chemical and
optical behavior of ordinary matter is determined by its outer or valence electrons. The remainder of the cloud is
ordinarily formed into “closed,” essentially unresponsive, shells around and tightly bound to the nucleus. These closed
or filled shells are made up of specific numbers of electron pairs. Even though it is not completely clear what occurs
internally when an atom radiates, we do know with some certainty that light is emitted during readjustments in the
outer charge distribution of the electron cloud. This mechanism is ultimately the predominant source of light in the
world.

Usually, an atom exists with its clutch of electrons arranged in some stable configuration that corresponds to their
lowest energy distribution or level. Every electron is in the lowest possible energy state available to it, and the atom as
a whole is in its so-called ground-state configuration. There it will likely remain indefinitely, if left undisturbed. Any
mechanism that pumps energy into the atom will alter the ground state. For instance, a collision with another atom,
an electron, or a photon can affect the atom’s energy state profoundly. An atom can exist with its electron cloud in
only certain specific configurations corresponding to only certain values of energy. In addition to the ground state,
there are higher energy levels, the excited states, each associated with a specific cloud configuration and a specific
well-defined energy. When one or more electrons occupies a level higher than its ground-state level, the atom is said
to be excited—a condition that is inherently unstable and temporary.
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At low temperatures, atoms tend to be in their ground state; at progressively higher temperatures, more and more of
them will become excited through atomic collisions. This sort of mechanism is indicative of a class of relatively gentle
excitations—glow discharge, flame, spark, and so forth—which energize only the outermost unpaired valence electrons.
We will initially concentrate on these outer electron transitions, which give rise to the emission of light, and the nearby
infrared and ultraviolet.
When enough energy is imparted to an atom (typically to the valence electron), whatever the cause, the atom can react
by suddenly ascending from a lower to a higher energy level , (Fig. below). The electron will make a very rapid transition,
a quantum jump, from its ground-state orbital configuration to one of the well-delineated excited states, one of the
quantized rungs on its energy ladder. As a rule, the amount of energy taken up in the process equals the energy
difference between the initial and final states, and since that is specific and well defined, the amount of energy that can
be absorbed by an atom is quantized (i.e., limited to specific amounts). This state of atomic excitation is a short-lived
resonance phenomenon. Usually, after about 10-8 s or 10-9 s, the excited atom spontaneously relaxes back to a lower
state, most often the ground state, losing the excitation energy along the way. This energy readjustment can occur by way
of the emission of light or (especially in dense materials) by conversion to thermal energy through interatomic collisions
within the medium. (This latter mechanism results in the absorption of light at the resonant frequency and the
transmission or reflection of the remaining frequencies—it’s responsible for most of the coloration in the world around
us.)
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If the atomic transition is accompanied by the emission of light (as it is in a rarefied gas), the energy of the photon
exactly matches the quantized energy decrease of the atom. That corresponds to a specific frequency, by way of
∆ℰ = ℎ𝜐, a frequency associated with both the photon and the atomic transition between the two particular states. This
is said to be a resonance frequency, one of several (each with its own likelihood of occurring) at which the atom very
efficiently absorbs and emits energy. The atom radiates a quantum of energy that presumably is created spontaneously,
on the spot, by the shifting electron.
ℎ𝜐
Ground state Excited state

3-3) Light in Bulk Matter

The response of dielectric or no conducting materials to electromagnetic fields is of special concern in Optics. We will, of
course, be dealing with transparent dielectrics in the form of lenses, prisms, plates, films, and so forth, not to mention
the surrounding sea of air.
The net effect of introducing a homogeneous, isotropic dielectric into a region of free space is to change 𝜀0 to 𝜀 and 𝜇0 to
𝜇 in Maxwell’s Equations. The phase speed in the medium now becomes

1
𝑣= (54)
𝜀𝜇
The ratio of the speed of an electromagnetic wave in vacuum to that in matter is known as the absolute index of
refraction n:
𝑐 𝜀𝜇
𝑛= =± = ± 𝑘𝐸 𝑘𝑚 (55)
𝑣 𝜀 0 𝜇0
Where n is usually positive.
There are magnetic substances that are transparent in the infrared and microwave regions of the spectrum. But we are
primarily interested in materials that are transparent in the visible, and these are all essentially “nonmagnetic.” Indeed,
𝑘𝑚 generally doesn’t deviate from 1.0 by any more than a few parts in 10-4. Setting 𝑘𝑚 = 1.0 in the formula for n results
in an expression known as Maxwell’s Relation, namely,
𝑛 ≈ 𝑘𝐸 (56)
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wherein 𝑘𝐸 is presumed to be the static dielectric constant. This relationship works well only for some simple gases. The
difficulty arises because 𝑘𝐸 and therefore n are actually frequency dependent. The dependence of n on the wavelength
(or color) of light is a well-known effect called dispersion.

Application
An EM wave travels through a homogeneous dielectric medium with a frequency of 𝑤 = 2.10 × 1015 𝑟𝑎𝑠/𝑠 and
𝑘 = 1.10 × 107 𝑟𝑎𝑑/𝑚. The 𝐸-field of the wave is
𝐸 = (180𝑒𝑦 )𝑒 𝑖(𝑘𝑥−𝑤𝑡)
Determine
a) The direction of 𝐵
b) The speed of the wave
c) The associated 𝐵-field
d) The index of refraction
e) The permittivity
f) The irradiance of the wave

Solution
Electromagnetic Theory and Photons / Chapter 1 P2205/2023/page44
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