Page 26 - Maxwell House

6 Chapter 1

other words, Maxwell’s equations solutions must be preserved against such “gauge
freedom. ” One of such “ gauge protector” is the electric charge conservation law, which
states that the charges can neither be created nor destroyed in an isolated system. Until
now no experimental data are challenging this law.
2. Electromagnetic energy conservation related to the symmetry under translation in time.
We must be sure that the same physical process exhibits the same outcomes regardless of
place or time (for example, electromagnetic wave propagation in free space are the same
at any time in America on a Monday or in Poland on a Sunday). This law means that the
total amount of any energy in an isolated system can be neither created nor lost, though
energy keeps the ability to transform from one form to another, to be transferred from one
object to another inside the isolated system. Even more importantly, the law of
electromagnetic energy conservation in the form of Poynting’s theorem leads to the
uniqueness of Maxwell’s equations solutions under certain like boundary conditions.
3. Linear momentum conservation related to the symmetry under translation in space. This
conservation law is the electrodynamics analog of Newton’s 3 law of motion - “Every
rd
action has an equal and opposite reaction.” Note that linear momentum is associated with
Poynting’s vector, which will be discussed later in Chapter 3, and radiation pressure
exerted upon physical objects. The reality of such pressure was proved experimentally by
Russian physicist Pyotr N. Lebedev in 1900.
4. Angular momentum conservation related to the symmetry under rotation in space. This law
is the rotation analog of linear momentum conservation law is the electrodynamics analog
of Newton's 1 law of motion - "A body continues in a state of rest or of uniform rotation
st
unless acted by an external torque." Note that angular momentum is associated with
Poynting’s vector, which will be discussed later in Chapter 3.

Why did we pay so much attention to energy consideration? “The study of energy has played a
pivotal role in understanding the creation of the universe, the origin of life, the evolution of
human civilization and culture, economic growth and the rise of living standards, war and
geopolitics, and significant environmental change at local, regional and global scales. Virtually
every discipline investigates some aspect of energy, including history, anthropology, public
policy, international relations, human and ecosystem health, economics, technology, physics,
geology, ecology, business management, environmental science, and engineering.”[1]
1.2.3 Nothing Exists Until It Is Measured

EM processes are mainly invisible. The only way to make it concrete and measurable is to
convert something invisible into readable data for an observer, using special sensors sensitive
to EM processes. Practically, all such sensors are based on an exchange between different forms
of energy while taking some energy from the monitored system. For example, a voltmeter as
shown in Figure 1.1.2 “seizes” a minute invisible portion of electrical current energy from
2
connected batteries and converts it into the kinetic energy of rotating coil in voltmeter and
visible movement of the pointer across a scale. As results, the EM phenomena, as with many
processes in physics associated with the storage or propagation of energy that can be measured,
becomes a reality through the measurements.

2 Public Domain Image, source: http://practicalphysics.org/learning-use-voltmeters.html