Elements of Electricity and Magnetism: Theory and Applications

Cover
Half Title
Title Page
Copyright Page
Preface
Table of Contents
1. Electric Charge and Coulomb’s Law
	1.1. Electric Charge
		1.1.1. Kinds of the Electric Charge
		1.1.2. The Unit of Charge
		1.1.3. Conservation of the Charge
	1.2. Electric Conductors and Insulators
	1.3. Coulomb’s Law of Force
	1.4. Limitations of Coulomb’s Law
	1.5. Superposition Principle
	1.6. Permittivity and Dielectric Constants
	Exercises
2. The Electrostatic Field
	2.1. The Electric Field
	2.2. Electric Field Due to Uniform Charge Distribution
	2.3. Motion of a Charged Particle in the Uniform Electric Field
	2.4. Electric Lines of Force (Properties of the Electric Field Line)
	2.5. Charge Densities
		(a) Volume Charge Density
		(b) Surface Charge Density
		(c) Line Charge Density
	2.6. The Electric Dipole
	2.7. The Electric Field Due to an Electric Dipole at a Point Along its Axis
	2.8. The Electric Field at a Point on the Perpendicular Bisector of the Dipole Axis
	2.9. An Electric Dipole in Uniform Electric Field
	2.10. An Electric Dipole in a Non-uniform Electric Field
	2.11. Potential Energy of Dipole in an Electric Field
	Exercises
3. Gauss’s Law
	3.1. Electric Flux
	3.2. Concept of Solid Angle
	3.3. Gauss’s Law of Electrostatics
	3.4. Gaussian Symmetrical Surfaces
	3.5. Electric Field of a Spherical Charge Distribution
	3.6. Electric Field of an Infinite Long Wire (Line Charge)
	3.7. Electric Field near an Infinite Plane Sheet
	3.8. Gauss’s Law in Differential Form
	3.9. Electric Field Due to Non-conducting Sphere
	3.10. Charge on Conductors
	Exercises
4. Electric Potentials
	4.1. Line Element and Line Integral
	4.2. Electric Potential and Potential Difference
	4.3. Electric Potential of a Point Charge
	4.4. Potential Due to Continuous Charge Distribution
	4.5. Negative Gradient of the Potential
	4.6. Electric Potential Due to a Dipole
	4.7. The Equipotential Surfaces
	4.8. Properties of Equipotential Surfaces
	4.9. Electric Potential Energy
	Exercises
5. Methods For the Solution of Electrostatic Problems
	5.1. Uniqueness Theorem
	5.2. Poisson’s and Laplace’s Equations
	5.3. Solution of Laplace’s Equation in Rectangular Coordinates
	5.4. Solution of Laplace’s Equation in Cylindrical Coordinates
	5.5. Solution of Laplace’s Equation in Spherical Polar Coordinates
	5.6. A Conducting Sphere in a Uniform Electric Field
	5.7. Method of Electrical Images
	5.8. Conducting Sphere
	Exercises
6. Capacitors and Dielectrics
	6.1. The Capacitor
		(a) Symbol
		(b) Types of Capacitor
		(c) Capacitance of a Capacitor
		(d) Unit of Capacitance
	6.2. Capacitance of a Parallel Plate Capacitor
	6.3. The Capacitance of an Isolated Conductor (Sphere)
	6.4. Capacitance of a Cylindrical Capacitor
	6.5. Series and Parallel Combinations of Capacitors
	6.6. Electrostatic Energy Stored in a Capacitor
	6.7. Force Between Plates of a Capacitor
	6.8. Electric Energy Stored in Conducting Sphere
	6.9. Dielectric Materials
	6.10. Polarisation
		(1) Polar Dielectrics
		(2) Non-polar Dielectrics
	6.11. Electric Field in Dielectrics
	6.12. Gauss’s law of Dielectrics
	6.13. Polarization Current Density
	6.14. Local Field in a Dielectric Material
	6.15. Dielectric Constant, Electric Susceptibility and Polarizability
	6.16. Clausius-Mossotti Equation
	6.17. Langevin equation of Polar-Dielectrics
	6.18. Energy Stored in a Dielectric
	6.19. Boundary Conditions at the Interface of two Dielectrics
	Exercises
7. Current, Resistance and Circuits
	7.1. Electric Current
	7.2. Current Density
	7.3. Resistance and Ohm’s law
	7.4. Superconductors
	7.5. Circuits Containing Resistors in Series and Parallel
		(a) Resistors in Series
		(b) Resistors in Parallel
	7.6. Electromotive Force and Single Loop Circuit
	7.7. Energy and Energy Dissipation in a Resistor
	7.8. Color Code for Carbon Resistor
	7.9. Kirchhoff’s Laws for Electric Networks
		(a) Junction Theorem
		(b) Loop or Mesh Theorem
	7.10. Matrix and Determinant Method for Solving Mesh Equations
	7.11. The RC Series Circuit
		(a) Charging of a Capacitor
		(b) Discharging of a Capacitor
	7.12. Potentio-meter
	7.13. Wheatstone’s Bridge
	Exercises
8. Magnetic Fields and Materials
	8.1. Magnets and the Magnetic Field
	8.2. Magnetic Flux
	8.3. Magnetic Force on a Moving Charge
	8.4. Motion of a Charge in a Uniform Magnetic Field
	8.5. Magnetic Force on a Current Carrying Conductor
	8.6. Magnetic Dipole Moment
	8.7. Magnetic Torque on a Current Loop
	8.8. Potential Energy of a dipole in a Magnetic Field
	8.9. The Biot-Savart Law
	8.10. Applications of Biot-Savart Law
		8.10.1. Magnetic Field Due to Long Straight Wire Carrying a Current
		8.10.2. Magnetic Field at the Centre of a Current Loop
		8.10.3. Magnetic Field Due to Current in a Finite Straight Conductor
		8.10.4. Magnetic Field Along the Axis of a Circular Coil
		8.10.5. Magnetic Field Along the Axis of a Long Solenoid
	8.11. Force Between Two Parallel Wires
	8.12. Ampere’s Law and Its Applications
	8.13. Magnetic Field of a Moving Point Charge
	8.14. Magnetic Field in Materials
		8.14.1. Magnetic Moment of an Electron
		8.14.2. Magnetic Permeability
		8.14.3. Magnetization
		8.14.4. Magnetic Susceptibility
		8.14.5. Diamagnetism
		8.14.6. Paramagnetism
		8.14.7. Ferromagnetism
		8.14.8. Hysteresis
		8.14.9. Hysteresis Loss
	Exercises
9. Alternating Currents
	9.1. Average and Root-Mean-Square Values of Voltage and Current
	9.2. Phasor Diagrams
	9.3. AC Circuit with Resistance
	9.4. AC Circuit with Capacitance
	9.5. AC Circuit with Industance
	9.6. AC Circuit with R and C in Series
	9.7. AC Circuit with R and L in Series
	9.8. Ac Circuit with L and C in Series
	9.9. AC Circuit with LCR in Series
	9.10. Series Resonance
	9.11. Power in AC Circuits
	9.12. AC Circuit with LCR in Parallel
	9.13. Quality Factor Q of Series Resonance
	9.14. Transformers
	Exercises
10. Time-Varying Fields
	10.1. Faraday’s Induction Law
	10.2. Lenz’s Law
	10.3. Fleming’s Right Hand Rule
	10.4. EMF Induced in a Moving Conductor
	10.5. EMF Induced in a Rotating Coil : Principle of Electric Generator
	10.6. Eddy Currents
	10.7. Self-Inductance
	10.8. Mutual Inductance
	10.9. Energy Stored in a Magnetic Field
	10.10. RL Circuit
	Exercise
11. Maxwell’s Equations and Electromagnetic Waves
	11.1. Maxwell’s Equations in Differential Form
	11.2. Displacement Current
	11.3. Maxwell’s Equations in Integral Form
	11.4. Maxwell’s Equations for Static Electric and Magnetic Fields
	11.5. Energy Flow in Electromagnetic Waves: Poynting Theorem
	11.6. Maxwell’s Equations for Free Space and Dielectric Media
	11.7. Maxwell’s Equations for Conducting Media
	11.8. Electromagnetic Wave Equation
	11.9. Plane Electromagnetic Waves in Free Space
	11.10. Plane Waves and Polarization
		(a) Linear Polarization
		(b) Circular Polarization
		(c) Elliptical Polarization
	11.11. Electromagnetic Waves in Conducting Media
	11.12. Scalar and Vector Potentials
	11.13. Non-Homogeneous Wave Equations for Vector and Scalar Potentials
	Exercises
Appendix A Physical Constants
Appendix B Trigonometrical Relations
Appendix C Algebraic Relations
Appendix D Vector Identities
Index