Electrodynamics: The Field-Free Approach

Electrodynamics: The Field-Free Approach
Electrostatics, Magnetism, Induction,
Relativity and Field Theory

The book starts by considering the different types of forces that occur between
electric charges. These may be directly related to their motion, i.e. charges at rest, in
uniform motion and in acceleration. The forces, known as electric, magnetic and inductive, are treated cohesively and formulated through observations and mea-surements. The subsequent chapters are more or less direct applications of the force formulas.

Chapter 3 introduces the energy concept as a direct consequence of force through
the principle of work. The inductive force is then utilized to derive magnetic energy. Neumann’s formula for inductance is fully derived and used to express
magnetic energy.

Chapter 4 covers macroscopic systems whose characteristics are obtained
through a summation of mutual interactions between infinitesimal elements of
charge. Calculation techniques for capacitance and inductance are introduced and
shown to be useful concepts in case the system is homogeneous.

Chapters 5 and 6 deal with the conductor and electric circuits which constitute
the experimental environment from which electrodynamics was developed and technical applications originated. The microscopic description of electric conduc-tion, the origin of resistance and its relation to heat are treated first. Then the resonance circuit which includes the other two circuit components, capacitance and inductance, is introduced.

Chapter 7 introduces electric and magnetic dipoles, which are significant con-cepts since nature generally may be described in terms of such objects. The

expressions for electric and magnetic dipole–dipole interaction energies are then
central to providing both force and torque.

Chapter 8 investigates how different electrically and magnetically neutral
materials respond to electric and magnetic influences. It is then assumed that the
material is composed of dipoles. The material parameters are introduced and
techniques for measuring them are described. A mathematically rigorous treatment
of the dipole, or generally multipole, interactions is presented in the accompanying
Appendices A and B.

In Chap. 9, it is shown conceptually how the magnetic and inductive dynamics
arise as motional consequences of the electric force assuming that interactions take
time; they are mediated at the speed of light. Alternatively, one may utilize the
knowledge of electric and magnetic forces to derive the speed of light. In a special
case both the magnetic force and the Faraday-Henry’s law of induction are derived.
It is also shown how electromagnetic dynamics is related to relativity, using the fact that magnetism is the motional consequence on which the special theory of rela- tivity is based. Since we build the theory upon the concept of force the material is unique to this book. Chapter 9 also introduces Lorentz transformation in the form of a tutorial. Prerequisites of Chap. 9 are only Chaps. 1–3, thus these four chapters may form a concise course in basic electrodynamics and its relation to relativity.

In Chap. 10, electromagnetic field theory is introduced and Maxwell's equations
formulated. The fields are indeed already defined by the force formulas, but
expressed in Maxwell’s equations in terms of their divergence and curl. This is
motivated by showing that the boundary conditions of the fields are then defined.
Using the fields, the Poynting vector may be formulated corresponding to the power
transported from an electrodynamic system.
An important feature of this book is thus that field theory is introduced after the physical phenomena that constitute electrodynamics have been described, inter-
preted and formulated in terms of fundamental forces.

In Chap. 11, antenna theory is introduced using the principle of retarded inter-
actions, i.e. taking into account that interactions take time. The small loop and the small wire antennas are treated assuming current is uniform and varies harmonically with time. Furthermore, the antenna array is discussed. The basic principles of retarded interactions and array effects are thus developed and may then be applied to natural oscillators as are found in nature. In this way, the reflection law, the refraction law and the phenomenon of Brewster reflection are derived and fully
explained. The power delivered by an antenna is also analysed using the Poynting vector derived in a previous chapter.

Appendix D contains solutions to the exercises appearing in the book.

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Prerequisites and Target Audience

Although electrodynamics is described in this book from its first principles, prior
knowledge of about one semester of university studies in mathematics and physics
is required, including vector algebra, integral and differential calculus as well as a
course in mechanics, treating Newton’s laws and the energy principle. The target
groups are teachers, engineering and physics students as well as professionals in the
field, e.g. high-school teachers and employees in the telecom industry. Also
chemistry and computer science students may benefit from the book.

Study Tips

Learning physics inevitably implies active involvement, especially in problem-
solving and experimental studies. We recommend that the discussed experiments

also be implemented in practice, not least to avoid tendencies to abstraction.
Some of the exercises, marked with an asterisk, are included in the theory of the
book and need to be solved before the chapter that follows them. The exercises
marked with a ‘C’ are more challenging and normally not suitable for independent
problem solving.
A solution manual is included in Appendix D.

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