Electrostatics : Tutorial (190,00 руб.)

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UDC 537.2(075) Published by the decision of the Editorial Review Board of the Kazan National Research Technological University Reviewers: Doctor of Engineering Sciences, Professor A. Turanov Ph.D. in Physics and Mathematics, Associate Professor I. Lunev Arkhipov V. Electrostatics : Tutorial / V. Arkhipov; The Ministry of Education and Science of the Russian Federation, Kazan National Research Technological University. – Kazan : KNRTU Press, 2024. – 88 p. ISBN 978-5-7882-3492-2 The tutorial outlines the main issues of the General Physics course (sections Electricity and Magnetism). It contains theoretical material on the topics: electric field, conductors and dielectrics in an electric field, electric field energy, analysis of solutions to typical problems, and self-check questions. The tutorial is intended for students studying Bachelor program 18.03.01 Chemical Technology of all specialties of mechanical and techno-logical profiles in order to strengthen the theoretical foundations of the General Physics course. The tutorial is prepared by the Department of Physics. 537.2(075) ISBN 978-5-7882-3492-2 © V. Arkhipov, 2024 © Kazan National Research Technological University, 2024 2

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CONTENTS Introduction ........................................................................................................... 5 1. ELECTRIC FIELD ........................................................................................... 9 1.1. Electric charge ...................................................................................... 9 1.2. Coulomb's law .................................................................................... 11 1.3. Electrostatic field strength .................................................................. 12 1.4. Electrostatic field potential ................................................................ 14 1.5. Theorem on the circulation of the field strength vector ..................... 16 1.6. Relationship between electric field strength and field potential ........ 17 1.7. Principle of electric field superposition ............................................. 18 1.8. Graphic representation of electrostatic fields .................................... 20 1.9. Ostrogradsky–Gauss theorem ............................................................ 22 1.10. Field of an infinite homogeneously charged plane. ......................... 24 1.11. Field of an infinite uniformly charged thread .................................. 26 1.12. Problems ........................................................................................... 27 Self-check questions .................................................................................. 34 2. CONDUCTORS IN AN ELECTROSTATIC FIELD ................................... 35 2.1. Properties of electron gas in metals ................................................... 35 2.2. Electric field inside and near the surface of the conductor ................ 36 2.3. Van de Graaff electrostatic generator ................................................ 39 2.4. Electrical induction and induced charges ........................................... 41 2.5. Electrostatic protection ....................................................................... 41 2.6. Capacitance ........................................................................................ 43 2.7. Problems ............................................................................................. 46 Self-check questions .................................................................................. 49 3. ELECTRIC FIELD IN DIELECTRICS .......................................................... 51 3.1. Electric dipole .................................................................................... 51 3.2. Dipole in a uniform electrostatic field ............................................... 53 3.3. Polarization of dielectrics ................................................................... 55 3.4. Mechanisms of polarization of dielectrics ......................................... 57 3.5. The relationship between dielectric susceptibility and permeability . 60 3.6. Electric displacement vector or electric induction vector .................. 61 3.7. Conditions on the interface between two dielectrics ......................... 62 3.8. Ferroelectrics or segnetoelectrics ....................................................... 65 3.9. Electrets .............................................................................................. 67 3.10. Problems ........................................................................................... 68 Self-check questions .................................................................................. 74 3

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4. ELECTRIC FIELD ENERGY ........................................................................ 75 4.1. Energy of a charged conductor .......................................................... 75 4.2. Energy of a system of fixed charged conductors ............................... 76 4.3. Energy of a dipole in an electric field ................................................ 77 4.4. Energy of a charged capacitor ............................................................ 78 4.5. Volumetric density of electric field energy ........................................ 79 4.6. Problems ............................................................................................. 80 Self-check questions .................................................................................. 84 Conclusion ........................................................................................................... 85 Bibliography ........................................................................................................ 86 4

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