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Rating: 
Summary: Review of A Promenade Along Electrodynamics
Review: Review of "A Promenade Along Electrodynamics," by Junichiro Fukai (Vales Lake Publishing,
Pueblo West, USA, 2003, ISBN: 0-9714845-1-1)Dr. Fukai of Auburn University published a remarkable book of 126 pages. It presents many
interesting ideas related with electromagnetism not covered by normal textbooks. It is divided in 9
chapters which run as follows: Introduction, Forces Between Two Charges Moving with Constant
Velocities, Comparison with Relativistic Treatment, Ampere's Force Law, High Speed Limit and
Comparison with the Special Theory of Relativity, Scattering and Orbit Problem, A More General
Theory - An Encounter with Weber's Force Law, Applications of Weber's Electrodynamics,
The Propagation of Electrical Signals in Vacuum. It ends with an Epilogue and two Appendices
including biographies of notable physicists in the 19th century, a good Bibliography and an Index. The book begins presenting Lorentz's force acting on a test charge in the presence of electric and
magnetic fields. This is the standard formula of classical electromagnetism but has some problems
of symmetry, lack of action and reaction, paradoxes which arise when we change frames of
reference etc. Some of these aspects are presented in the introduction of the book. It is then
followed by a new force formula to replace Lorentz's expression, which avoids these paradoxes.
The new expression is compared with standard relativistic treatment for the interaction between
moving charges. In Chapter 4 the author presents Ampere's force law between current elements. Only by this
fact this book should be read by all specialists and students of electrodynamics. The reason is that
Ampere's expression has been forgotten and is not to be found in most textbooks dealing with
electrodynamics, which only present Grassmann's force (based on Biot-Savart's expression of the
magnetic field of a current element and compatible with Lorentz's force). Despite this fact is should
be remembered that Maxwell himself knew both expresssions for the force between current elements
(those of Ampere and Grassmann). In his masterpiece, A Treatise
on Electricity and Magnetism, Vol. 2, page 174, paragraph 527, Maxwell compared these expressions
and concluded that Ampere's force is undoubtedly the best, since it made the forces on the two elements
not only equal and opposite but in the straight line which joins them. Grassmann's force, on the other hand,
does not comply with action and reaction (the same as regards Lorentz's force). In the next page,
paragraph 528, Maxwell said that Ampere's force should always remain the cardinal formula of
electrodynamics. Modern books dealing with electromagnetism have forgotten about this and present
only Grassmann's problematic expression. Fukai suceeds in deriving Ampere's force from his own more
basic expression which deals with the interaction between point charges. He also discusses Rutherfod
scattering formula and the orbit problem for two charges interacting with one another. Chapters 7 and 8 are devoted to Weber's electrodynamics and applications of this fascinating theory
which was proposed by Maxwell's contemporary Wilhelm Weber, who worked in Goettingen in
collaboration with Carl Friedrich Gauss (the same Weber of the magnetic flux unit). Weber's force is
an extension of Coulomb's expression including terms which depend on the relative velocity and
acceleration between the interacting bodies. Weber introduced in his expression the fundamental constant
c and was the first to measure it in collaboration with Kohlrausch, finding essentially the same value
as light velocity in vacuum, indicating a connection between electrodynamics and optics. All of this
was done before Maxwell and his electromanetic theory of light. Weber and Kirchhoff also suceeded
in deriving the telegraphy equation for a disturbance propagating along a wire which predicted the
propagation of the signal in wires of negligible resistance at light velocity, once more before Maxwell!
All of this is almost unknown nowadays but is discussed at length in Fukai's fascinating work. He
also extends this work for the propagation of electrical signals in vacuum by considering it as composed
of pairs of positive and negative charges. Fukai's
also shows in details the compatibility of Weber's force with Maxwell's equations (but not with
Lorentz's force law). He presents some possible experimental tests to distinguish Weber's force
from Lorentz's force with great clarity and giving orders of magnitude. I recommend strongly the careful reading of this book which can initiate a new revolution in
electrodynamics. It has many new ideas and insights, is full of historical information, is rich in modern
experimental and theoretical references. And above all, is non dogmatic, presenting the concepts for
the reflection of the readers in clear form and inspiring contents. Andre Koch Torres Assis
Institute of Physics
State University of Campinas
13083-970 Campinas, Sao Paulo, Brazil
Email: assis@ifi.unicamp.br
Homepage: http://www.ifi.unicamp.br/~assis
Rating:
Summary: Review of A Promenade Along Electrodynamics
Review: Review of "A Promenade Along Electrodynamics," by Junichiro Fukai (Vales Lake Publishing,
Pueblo West, USA, 2003, ISBN: 0-9714845-1-1) Dr. Fukai of Auburn University published a remarkable book of 126 pages. It presents many
interesting ideas related with electromagnetism not covered by normal textbooks. It is divided in 9
chapters which run as follows: Introduction, Forces Between Two Charges Moving with Constant
Velocities, Comparison with Relativistic Treatment, Ampere's Force Law, High Speed Limit and
Comparison with the Special Theory of Relativity, Scattering and Orbit Problem, A More General
Theory - An Encounter with Weber's Force Law, Applications of Weber's Electrodynamics,
The Propagation of Electrical Signals in Vacuum. It ends with an Epilogue and two Appendices
including biographies of notable physicists in the 19th century, a good Bibliography and an Index. The book begins presenting Lorentz's force acting on a test charge in the presence of electric and
magnetic fields. This is the standard formula of classical electromagnetism but has some problems
of symmetry, lack of action and reaction, paradoxes which arise when we change frames of
reference etc. Some of these aspects are presented in the introduction of the book. It is then
followed by a new force formula to replace Lorentz's expression, which avoids these paradoxes.
The new expression is compared with standard relativistic treatment for the interaction between
moving charges. In Chapter 4 the author presents Ampere's force law between current elements. Only by this
fact this book should be read by all specialists and students of electrodynamics. The reason is that
Ampere's expression has been forgotten and is not to be found in most textbooks dealing with
electrodynamics, which only present Grassmann's force (based on Biot-Savart's expression of the
magnetic field of a current element and compatible with Lorentz's force). Despite this fact is should
be remembered that Maxwell himself knew both expresssions for the force between current elements
(those of Ampere and Grassmann). In his masterpiece, A Treatise
on Electricity and Magnetism, Vol. 2, page 174, paragraph 527, Maxwell compared these expressions
and concluded that Ampere's force is undoubtedly the best, since it made the forces on the two elements
not only equal and opposite but in the straight line which joins them. Grassmann's force, on the other hand,
does not comply with action and reaction (the same as regards Lorentz's force). In the next page,
paragraph 528, Maxwell said that Ampere's force should always remain the cardinal formula of
electrodynamics. Modern books dealing with electromagnetism have forgotten about this and present
only Grassmann's problematic expression. Fukai suceeds in deriving Ampere's force from his own more
basic expression which deals with the interaction between point charges. He also discusses Rutherfod
scattering formula and the orbit problem for two charges interacting with one another. Chapters 7 and 8 are devoted to Weber's electrodynamics and applications of this fascinating theory
which was proposed by Maxwell's contemporary Wilhelm Weber, who worked in Goettingen in
collaboration with Carl Friedrich Gauss (the same Weber of the magnetic flux unit). Weber's force is
an extension of Coulomb's expression including terms which depend on the relative velocity and
acceleration between the interacting bodies. Weber introduced in his expression the fundamental constant
c and was the first to measure it in collaboration with Kohlrausch, finding essentially the same value
as light velocity in vacuum, indicating a connection between electrodynamics and optics. All of this
was done before Maxwell and his electromanetic theory of light. Weber and Kirchhoff also suceeded
in deriving the telegraphy equation for a disturbance propagating along a wire which predicted the
propagation of the signal in wires of negligible resistance at light velocity, once more before Maxwell!
All of this is almost unknown nowadays but is discussed at length in Fukai's fascinating work. He
also extends this work for the propagation of electrical signals in vacuum by considering it as composed
of pairs of positive and negative charges. Fukai's
also shows in details the compatibility of Weber's force with Maxwell's equations (but not with
Lorentz's force law). He presents some possible experimental tests to distinguish Weber's force
from Lorentz's force with great clarity and giving orders of magnitude. I recommend strongly the careful reading of this book which can initiate a new revolution in
electrodynamics. It has many new ideas and insights, is full of historical information, is rich in modern
experimental and theoretical references. And above all, is non dogmatic, presenting the concepts for
the reflection of the readers in clear form and inspiring contents. Andre Koch Torres Assis
Institute of Physics
State University of Campinas
13083-970 Campinas, Sao Paulo, Brazil
Email: assis@ifi.unicamp.br
Homepage: http://www.ifi.unicamp.br/~assis
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