Electromagnetism: With Solved Problems

✍ Scribed by Hiqmet Kamberaj

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 400
• Series: Undergraduate Texts in Physics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Electromagnetism; electrostatics; magnetism; electromagnetic waves; Coulomb; Gauss; Maxwell; Ohm; Biot-Savart; Ampere; Faraday; Fresnel; Lorentz