Electromagnetism: With Solved Problems (Undergraduate Texts in Physics)

Physics is part of any curriculum in science and engineering. The main objective of this course is to help students of engineering and other sciences in more advanced courses in these fields. The textbook will introduce the students to the fundamental concepts of physics and how different theories developed from physical observations and phenomena. It starts with electrostatics in free space, introducing basic concepts, such as Coulomb's electric charge law and ideas of electric field and electric field lines (Chapter 1). Chapter 2 introduces the electric flux and Gauss's law. Electrostatic potential and electrostatic potential energy are introduced in Chapter 3. Chapter 4 presents the concepts of capacitance and dielectrics. Also, the electrostatics of a macroscopic medium and Maxwell's equations of the electrostatic field are discussed. Chapter 5 introduces the concepts of electric current and Ohm's law. Chapter 6 continues with the magnetic field and its interactions with charges and currents. Then, Chapter 7 introduces the concept of magnetic field sources, where Biot-Savart law and Ampère's law are introduced. Chapter 8 describes magnetism in the medium, Faraday's law, and Maxwell's magnetic field equations. Then, Chapter 9 describes Maxwell's equations of electromagnetic fields. In particular, this chapter focuses on the potential vector and scalar of the electromagnetic field, electromagnetic field energy, and conservation laws. Then, the dynamics of charged particles in the electromagnetic field and averaging of microscopic properties to obtain the macroscopic Maxwell's equations are introduced. Chapter 10 describes some advancing topics on the induction law and alternating current circuit systems, aiming at understanding electromagnetism applications to wireless charging. Chapter 11 introduces some applications of the theory of electromagnetism in macromolecular solutions and wireless charging technology. Chapter 12 introduces electromagnetic waves in vacuum and medium, coherence of electromagnetic waves, the polarization of electromagnetic waves, reflection and refraction of electromagnetic waves, and Fresnel's equations. Chapter 13 introduces electromagnetic wave equations in dispersive media. This chapter also describes the absorption, Lorentz's oscillator model of a dielectric, the wave equation of a conductor, the wave equation of a dilute plasma, and the magnetized plasma or dielectric. Besides, Appendix introduces some mathematical background in vector analysis and vector differential operators. The textbook is geared more towards examples and problem-solving techniques. The students will get a firsthand experience of how the theories in physics are applied to problems in engineering and science. The textbook is mainly aimed at undergraduate students in engineering and science. However, some chapters and sections are aimed at senior undergraduate students working in the final year thesis in theoretical and computational biophysics, physics, electrical and electronic engineering, and chemistry. Preface Contents 1 Electrostatics in Free Space 1.1 Electrical Charges 1.2 Coulomb's Law 1.3 Coulomb's Law for a System of Charges 1.4 Electric Field 1.4.1 Force Fields 1.4.2 Superposition Principle 1.5 Electric Field Lines 1.6 Motion in Uniform Electric Field 1.7 Exercises Reference 2 Gauss's Law 2.1 Electric Flux 2.1.1 Uniform Electric Field 2.1.2 General Electric Field Flux 2.2 Gauss's Law 2.2.1 Gauss's Law for a System of Charges 2.3 Applications of Gauss's Law to Insulators 2.4 Conductors in Electrostatic Equilibrium 2.4.1 Property 1 2.4.2 Property 2 2.4.3 Property 3 2.4.4 Property 4 2.5 Exercises Reference 3 Electrostatic Potential 3.1 Electrostatic Potential Energy 3.2 Electric Potential 3.3 Potential Difference in a Uniform Electric Field 3.4 Equipotential Surface 3.5 Electric Potential of a Point Charge 3.6 Electric Potential of a System of Point Charges 3.7 Electric Potential of a Continuous Charge Distribution 3.8 Differential form of Electric Potential 3.9 Multipole Expansion 3.10 Electric Potential of a Charged Conductor 3.10.1 Cavity Within a Conductor 3.11 Exercises References 4 Capacitance and Dielectrics 4.1 Capacitance 4.2 Calculating Capacitance 4.2.1 Spherical Conductors 4.2.2 Parallel-Plate Capacitors 4.3 Combination of Capacitors 4.3.1 Parallel Combination 4.3.2 Series Combination 4.4 Energy Storage in the Electric Field 4.5 Electrostatics of Macroscopic Media and Dielectrics 4.5.1 Dielectrics 4.5.2 Comparison Between Dielectric Materials and Conductors 4.5.3 Molecular Theory of Dielectrics 4.5.4 Energy Stored in Capacitor 4.6 Electric Polarization 4.7 Set of Maxwell Equations for Electrostatic Field 4.7.1 Maxwell Equations for Free Space Electrostatic Field 4.7.2 Maxwell Equations for Dielectric Media Electrostatic Field 4.8 Potential Energy of Electrostatic Field 4.9 Exercises References 5 Electric Current 5.1 Electric Current 5.1.1 Direction of Electric Current 5.1.2 Charge Carrier 5.2 Microscopic Model of Current 5.3 Resistance and Ohm's Law 5.3.1 Ohm's Law 5.3.2 Classical Model for Electrical Conduction 5.3.3 Resistance and Temperature 5.4 Superconductors 5.5 Electric Energy and Power 5.6 Electromotive Force 5.7 Exercises Reference 6 Magnetic Field 6.1 Magnetic Field 6.2 Magnetic Force Acting on a Current-Carrying Conductor 6.3 Torque on a Current Loop in a Uniform Magnetic Field 6.4 Motion of a Charged Particle in a Uniform Magnetic Field 6.5 Exercises Reference 7 Sources of Magnetic Field 7.1 Biot-Savart Law 7.2 Magnetic Force Between Two Parallel Conductors 7.3 Ampére's Law 7.4 Magnetic Flux 7.5 Gauss's Law in Magnetism 7.6 Displacement Current 7.7 Exercises References 8 Magnetism in Matter 8.1 Magnetic Moments of Atoms 8.2 Magnetization Vector and Magnetic Field Strength 8.3 Classification of Magnetic Substances 8.3.1 Ferromagnetism 8.3.2 Paramagnetism 8.3.3 Diamagnetism 8.4 The Magnetic Field of the Earth 8.5 Faraday's Law of Induction 8.6 Rowland Ring Apparatus 8.7 Maxwell's Equations of Magnetism 8.8 Vector Potential 8.9 Multipole Expansion 8.10 Energy of the Magnetic Field 8.11 Exercises References 9 Maxwell's Equations of Electromagnetism 9.1 Maxwell's Equations of Electromagnetism 9.2 Vector and Scalar Potentials of Electromagnetic Field 9.3 Electromagnetic Field Energy and Conservation Law 9.4 Conservation Law of Momentum 9.5 Dynamics of Charged Particles in Electromagnetic Fields 9.6 Macroscopic Maxwell Equations 9.7 Exercises References 10 More About Faraday's Law of Induction 10.1 Moving Conductor in a Closed Circuit 10.1.1 Induced Electric Potential and Electric Field 10.1.2 Generators and Motors 10.2 Inductance 10.2.1 Self-inductance 10.2.2 Mutual Inductance 10.3 Oscillations in an LC Circuit 10.4 The RL Circuit 10.5 The RLC Circuit 10.5.1 Case 1 10.5.2 Case 2 10.5.3 Case 3 10.6 Alternating Current Circuits 10.6.1 AC Sources and Phases 10.6.2 Resistors in an AC Circuit 10.6.3 Inductors in an AC Circuit 10.6.4 Capacitors in an AC Circuit 10.6.5 The RLC Series in an AC Circuit 10.7 Power in the AC Circuit 10.8 Resonance in the RLC Series Circuit 10.9 Exercises Reference 11 Some Applications of Electromagnetic Theory 11.1 Electrostatic Properties of Macromolecular Solutions 11.1.1 The pH and Equilibrium Constant 11.1.2 Charge on DNA and Proteins 11.1.3 Charge States of Amino Acids 11.1.4 Salt Binding 11.1.5 Energy Cost of Assembling a Collection of Charges 11.1.6 The Poisson-Boltzmann Equation 11.1.7 Calculation of pKa of Amino Acids in Macromolecules 11.2 Wireless Charging 11.2.1 Tightly Coupled Wireless Power Systems 11.2.2 Loosely Coupled Highly Resonant Systems 11.3 Exercises References 12 Electromagnetic Waves in Vacuum and Linear Medium 12.1 Electromagnetic Wave Equations in Vacuum 12.2 Relationships Between k, E, B 12.3 Electromagnetic Waves Equations in Linear Medium 12.4 Energy and Momentum of Electromagnetic Waves 12.5 Coherence of Electromagnetic Waves 12.6 Polarization of Electromagnetic Waves 12.6.1 Linear Polarization 12.6.2 Circular and Elliptical Polarization 12.7 Reflection and Refraction of Electromagnetic Waves 12.7.1 Laws of Reflection and Refraction 12.8 Fresnel Equations 12.8.1 Boundary Conditions 12.8.2 Perpendicular Polarization 12.8.3 Parallel Polarization 12.8.4 External and Internal Reflection 12.8.5 Normal Incidence of Electromagnetic Waves 12.8.6 Reflectance and Transmittance 12.9 Exercises References 13 Electromagnetic Waves in Dispersive Media 13.1 Dispersion and Absorption 13.1.1 Lorentz's Model of Oscillations in Dielectrics 13.2 Dispersion 13.2.1 Wave Packets and Group Velocity 13.2.2 Normal and Anomalous Dispersion 13.3 Refractive Index of a Conductor 13.4 Wave Propagation in a Dilute Plasma 13.4.1 Electromagnetic Waves in a Dilute Plasma 13.4.2 Phase and Group Velocity in a Dilute Plasma 13.4.3 Plasma and Dielectric at High Frequency 13.5 Exercises References Appendix Vectorial Analysis A.1 Vector Calculus A.2 Vector Differential Operators A.3 Stokes' Formula A.4 Gauss's Formula A.5 Some Useful Formula A.6 Laplacian A.7 Curvilinear Coordinates Any curriculum involving science and/or engineering will eventually find itself entering the realm of physics. This book seeks to introduce students to a number of the fundamental concepts in physics and illustrate how different theories were developed out of physical observations and phenomena. The book presents multi-chapter sections on electrostatics, magnetism and electromagnetic waves, with eyes on both the past and the future, touching, along the way, on Coulomb, Gauss, Maxwell, Ohm, Biot-Savart, Ampere, Faraday, Fresnel and Lorentz. The book also contains an appendix that provides the reader with a portion of the mathematical background of vector analysis and vector differential operators. The book approaches its topics through a focus on examples and problem-solving techniques, illustrating vividly how physical theories are applied to problems in engineering and science. The book is primarily aimed at undergraduate students in these two fields, but it also features chapters that are geared towards senior undergraduates working on their final year theses.