Scope of this Course
Electromagnetism
In the previous course you studied what is usually called Newtonian
mechanics. In that part of classical physics the emphasis is on particles,
their interactions with each other, and the overall behavior of systems of
particles. To analyze the behavior of a system one identifies all the forces
acting and gives to each of them a mathematical description, often
simplified by making approximations. Through Newton's 2nd law the
motion of the system then becomes a matter of mathematical analysis.
Only in the study of gravity was the concept of a field given much
mention, and even in that case the main emphasis was on effects of the
field on particles (or satellites).
In this course you will study discoveries made mostly in the 19th century.
The story of how scientists gradually found the laws governing electric
and magnetic phenomena is full of the interplay between important
experimental discoveries and significant shifts in the theoretical
framework. Chief among the latter is the emergence of the idea of fields.
This is a course mainly about the electromagnetic field. Even in the
discussion of light and optics we will often use the fact that light is a
wave phenomenon in the electromagnetic field.
Before 1800 there were three distinct branches of physics covering our
area of study: electricity, magnetism and optics. By 1900 all three were
understood as different aspects of the electromagnetic field. The century
between those dates saw a long list of scientific achievements of great
importance, to technology as well as pure science. These greatly enriched
our understanding of nature, and led to technological advances that
transformed the quality of life. Everyday life had changed relatively little
between antiquity and 1800. But by 1900 (and much more so by 2000)
there had been dramatic changes. The principal cause of these changes
was the practical application of our new knowledge of the laws of
electromagnetism. These applications rank with the taming of fire among
mankind's most important accomplishments.
At the end we will quickly survey some of the discoveries made after
1895 about the structure of matter, especially of atoms and nuclei. In the
process we will touch on the revolutionary changes in our approach to
understanding nature, those that led to quantum theory.
The Electrostatic Field
Our description starts with the electrostatic field, which involves electric
phenomena affecting bodies more or less at rest. This field is much like
gravity, with the important difference that electric charge (unlike mass)
can take on either positive or negative values, so the fundamental force
can be either an attraction (like gravity) or a repulsion.
Like gravity, the electrostatic force is conservative, so we define its
potential energy. An important auxiliary scalar field called electrostatic
potential is introduced.
As always, energy is of prime importance in our understanding of things.
We will discuss the energy in the electrostatic field, especially in terms of
capacitors which store it.
Currents and Circuits
The flow of electric charge called current is described, and practical
arrangements using that flow in a controlled way, called circuits, are
discussed. At first only currents constant in time are considered. Later,
time-dependent currents are analyzed, especially those that oscillate
sinusoidally.
The Magnetic Field
The magnetic field, as it affects individual moving charged particles or
currents in circuits, is described next. Then we discuss the way in which a
current acts as the source of a magnetic field.
The magnetic properties of materials are not treated in detail because a
serious discussion of that subject necessarily involves quantum theory.
Electrodynamics
Up to this point, the fields are assumed to be independent of time, and act
independently of each other. When time-varying fields are considered,
remarkable new phenomena appear, linking electricity with magnetism.
The first of these is the induction of a current — or more fundamentally
an electric field — by a time-varying magnetic field. There is also a
corresponding induction of a magnetic field by a time-varying electric
field. In combination, these phenomena make possible transport of
energy and momentum through empty space by means of
electromagnetic waves .
The description of electromagnetism is now complete, embodied in the
famous equations put forward by Maxwell, plus the equation due to
Lorentz describing how the fields act on a single charged particle.
Optics
Systematic study of light dates back at least to the 17th century, but only
in the 19th did it become clear that light is a particular type of
electromagnetic wave.
Our discussion begins with the approximation called "ray" optics, which
is based on the fact that the wavelengths of visible light are very small by
human standards. This subject includes analysis of reflection and
refraction at interfaces between two media, and deals with formation of
optical images by devices, such as mirrors and lenses, using these
phenomena.
Then we study those phenomena specifically exhibiting the
electromagnetic wave properties of light, including polarization,
interference and diffraction.
Atomic and Nuclear Physics
The course closes with a brief discussion of atomic and nuclear physics,
surveying some of the discoveries made in the 20th century about the
microscopic world.
Although atoms and molecules were assumed to exist by most scientists
(especially chemists) in the 19th century, direct evidence for them came
only at the end of that century. The discovery of the electron in 1897
began a century of exploration of the structure of these objects. A major
breakthrough was the discovery in 1911 of the atomic nucleus.
It was clear early on that the rules of classical physics could not
adequately deal with these microscopic systems. By the end of the 1920's
a new framework, quantum mechanics, was developed that seems to
provide the appropriate theoretical basis. Soon many of the mysteries of
atomic structure were being explained. We will discuss a few of these.
In the1930's the structure and properties of the nucleus came under
intense investigation. Some of the processes peculiar to the nucleus, such
as radioactivity, have great importance in modern medical practice. We
will discuss a few of these properties.