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Published:2021
John Lekner, "Front Matter", Electrostatics of Conducting Cylinders and Spheres, John Lekner
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Written by a recognized expert in the field, Electrostatics of Conducting Cylinders and Spheres presents the theory in a simple and physical way, beginning with basic principles and moving onto the details of electrostatics of pairs of spheres and of pairs of cylinders. The difficult topic of a finite charged cylinder is also covered. The book presents exact solutions, in closed form where possible, with recent and new results included. Applications to engineering, physical, chemical, and biological problems are also presented.
Key topics include:
Fundamentals of the polarizability tensor and capacitance coefficients of an assembly of conductors.
Rigorous and thorough theoretical investigation of the electrostatics of spheres and cylinders.
Uniform formalism used in the solution for a rich array of problems.
Theoretical and experimental physicists, chemists, and engineers will find this an invaluable reference. It is also suitable for advanced undergraduate and graduate students in electrodynamics.
In memory of my mother
Preface
The aim of this monograph is to present the electrostatics of conducting cylinders and spheres in a simple and physical way, from first principles. The book can be just nine chapters because the subject matter is restricted almost exclusively to pairs of cylinders and spheres. The notable exception is a chapter on the difficult electrostatics of a solitary finite cylinder.
The electrostatics of an isolated sphere is one of the possible opening topics of books on electromagnetism, but two spheres already present some mathematical difficulty. A natural system of coordinates is the bispherical one, in which one of the two bispherical variables is (a different) constant on each of the two sphere surfaces. An analogous and closely related system, bicylindrical coordinates, makes two-cylinder electrostatic problems analytically tractable.
The solution of the two-sphere problem gives an unexpected result: if both are charged positively or if both are charged negatively, they will in general attract at very short range.
The chapters are on fundamentals, bispherical coordinates, two spheres in an external field, two charged spheres, bicylindrical coordinates, two cylinders in an external field, two charged cylinders, the solitary finite cylinder mentioned above, and a final chapter which gives details of some of the mathematical methods used in the book.
The book considers cylinders and spheres as ideal conductors of fixed shape. The real world is more complicated, of course. For example, droplets in suspension will not be perfect conductors, and are deformable in interesting ways. Chapters 3 and 4 (on spheres) and 6 and 7 (on cylinders) have sections discussing applications to problems in physics, chemistry, engineering, and biophysics.
Wellington, New Zealand
March 2021
Acknowledgments
Thanks are due to Dr. Rufus Boyack, who has read the entire final draft and provided a very welcome list of corrections. It has been my good fortune to have had Rufus as student, collaborator, and tutor.