# Schaum's Outline of Electromagnetics, Fifth Edition

by: Mahmood Nahvi, Joseph A. Edminister

**Abstract:**Tough test questions? Missed lectures? Not enough time? Fortunately, there's Schaum's. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you: • Hundreds of supplementary problems to reinforce knowledge • Concise explanations of all electromagnetic concepts • Information on current density, capacitance, magnetic fields, inductance, electromagnetic waves, transmission lines, and antennas • New section on transmission line parameters • New section illustrating the use of admittance plane and Smith Chart • New section on impedance transformation • New chapter on sky waves, attenuation and delay effects in troposphere, line-of-sight propagation, and other relevant topics • Support for all major textbooks for courses in electromagnetics PLUS: Access to revised Schaums.com website with 24 problem-solving videos, and more. Schaum's reinforces the main concepts required in your course and offers hundreds of practice questions to help you succeed. Use Schaum's to shorten your study time and get your best test scores!

Full details

## Table of Contents

**A.**Preface**1.**The Subject of Electromagnetics**2.**Vector Analysis**3.**Electric Field**4.**Electric Flux**5.**Gradient, Divergence, Curl, and Laplacian**6.**Electrostatics: Work, Energy, and Potential**7.**Electric Current**8.**Capacitance and Dielectric Materials**9.**Laplace's Equation**10.**Magnetic Field and Boundary Conditions**11.**Forces and Torques in Magnetic Fields**12.**Inductance and Magnetic Circuits**13.**Time-Varying Fields and Maxwell's Equations**14.**Electromagnetic Waves**15.**Transmission Lines**16.**Waveguides**17.**Antennas**18.**Propagation of Electromagnetic Waves in the Atmosphere**A.**APPENDIX

## Tools & Media

## Expanded Table of Contents

**A.**Preface**1.**The Subject of Electromagnetics- Historical Background
- Objectives of the Chapter
- Electric Charge
- Units
- Vectors
- Electrical Force, Field, Flux, and Potential
- Magnetic Force, Field, Flux, and Potential
- Electromagnetic Induction
- Mathematical Operators and Identities
- Maxwell's Equations
- Electromagnetic Waves
- Trajectory of a Sinusoidal Motion in Two Dimensions
- Wave Polarization
- Electromagnetic Spectrum
- Transmission Lines
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS
- ANSWERS TO SUPPLEMENTARY PROBLEMS
- SOME REFERENCES FOR HISTORICAL BACKGROUND

**2.**Vector Analysis**3.**Electric Field**4.**Electric Flux**5.**Gradient, Divergence, Curl, and Laplacian- Introduction
- Gradient
- The Del Operator
- The Del Operator and Gradient
- Divergence
- Expressions for Divergence in Coordinate Systems
- The Del Operator and Divergence
- Divergence of D
- The Divergence Theorem
- Curl
- Laplacian
- Summary of Vector Operations
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS
- ANSWERS TO SUPPLEMENTARY PROBLEMS

**6.**Electrostatics: Work, Energy, and Potential- Work Done in Moving a Point Charge
- Conservative Property of the Electrostatic Field
- Electric Potential between Two Points
- Potential of a Point Charge
- Potential of a Charge Distribution
- Relationship between E and V
- Energy in Static Electric Fields
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS
- ANSWERS TO SUPPLEMENTARY PROBLEMS

**7.**Electric Current**8.**Capacitance and Dielectric Materials- Polarization P and Relative Permittivity ϵr
- Capacitance
- Multiple-Dielectric Capacitors
- Energy Stored in a Capacitor
- Fixed-Voltage D and E
- Fixed-Charge D and E
- Boundary Conditions at the Interface of Two Dielectrics
- Method of Images
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS
- ANSWERS TO SUPPLEMENTARY PROBLEMS

**9.**Laplace's Equation- Introduction
- Poisson's Equation and Laplace's Equation
- Explicit Forms of Laplace's Equation
- Uniqueness Theorem
- Mean Value and Maximum Value Theorems
- Cartesian Solution in One Variable
- Cartesian Product Solution
- Cylindrical Product Solution
- Spherical Product Solution
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS
- ANSWERS TO SUPPLEMENTARY PROBLEMS

**10.**Magnetic Field and Boundary Conditions- Introduction
- Biot-Savart Law
- Ampère's Law
- Relationship of J and H
- Magnetic Flux Density B
- Boundary Relations for Magnetic Fields
- Current Sheet at the Boundary
- Summary of Boundary Conditions
- Vector Magnetic Potential A
- Stokes' Theorem
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS
- ANSWERS TO SUPPLEMENTARY PROBLEMS

**11.**Forces and Torques in Magnetic Fields**12.**Inductance and Magnetic Circuits- Inductance
- Standard Conductor Configurations
- Faraday's Law and Self-Inductance
- Internal Inductance
- Mutual Inductance
- Magnetic Circuits
- The B-H Curve
- Ampère's Law for Magnetic Circuits
- Cores with Air Gaps
- Multiple Coils
- Parallel Magnetic Circuits
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS
- ANSWERS TO SUPPLEMENTARY PROBLEMS

**13.**Time-Varying Fields and Maxwell's Equations- Introduction
- Maxwell's Equations for Static Fields
- Faraday's Law and Lenz's Law
- Conductors' Motion in Time-Independent Fields
- Conductors' Motion in Time-Dependent Fields
- Displacement Current
- Ratio of Jc to JD
- Maxwell's Equations for Time-Varying Fields
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS
- ANSWERS TO SUPPLEMENTARY PROBLEMS

**14.**Electromagnetic Waves- Introduction
- Wave Equations
- Solutions in Cartesian Coordinates
- Plane Waves
- Solutions for Partially Conducting Media
- Solutions for Perfect Dielectrics
- Solutions for Good Conductors; Skin Depth
- Interface Conditions at Normal Incidence
- Oblique Incidence and Snell's Laws
- Perpendicular Polarization
- Parallel Polarization
- Standing Waves
- Power and the Poynting Vector
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS
- ANSWERS TO SUPPLEMENTARY PROBLEMS

**15.**Transmission Lines- Introduction
- Distributed Parameters
- Incremental Models
- Transmission Line Equation
- Impedance, Admittance, and Other Features of Interest
- Sinusoidal Steady-State Excitation
- Lossless Lines
- The Smith Chart
- Admittance Plane
- Quarter-Wave Transformer
- Impedance Matching
- Single-Stub Matching
- Double-Stub Matching
- Impedance Measurement
- Transients in Lossless Lines
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS
- ANSWERS TO SUPPLEMENTARY PROBLEMS

**16.**Waveguides**17.**Antennas- Introduction
- Current Source and the E and H Fields
- Electric (Hertzian) Dipole Antenna
- Antenna Parameters
- Small Circular-Loop Antenna
- Finite-Length Dipole
- Monopole Antenna
- Self- and Mutual Impedances
- The Receiving Antenna
- Linear Arrays
- Reflectors
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS
- ANSWERS TO SUPPLEMENTARY PROBLEMS

**18.**Propagation of Electromagnetic Waves in the Atmosphere- Introduction and Summary
- Plane Waves in Homogeneous Media
- Propagation Parameters
- Complex Dielectric Constant
- Power Equation
- Refraction
- Reflection, Diffraction, and Scattering
- The Atmosphere
- Atmospheric Effects on Propagation of Radio Waves
- Attenuation by Gaseous Absorption
- Attenuation by Hydrometeors
- Ground and Sky Waves
- Models of the Troposphere
- Tropospheric Refractivity
- Tropospheric Excess Delay
- Bending Effect of Tropospheric Refraction
- Conductivity, Permittivity, and Refraction Index of the Ionosphere
- Satellite Microwave Ranging
- Ionospheric Range Error
- Tropospheric Range Error
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS
- ANSWERS TO SUPPLEMENTARY PROBLEMS
- Selected References for Further Reading

**A.**APPENDIX

**Book Details**

**Title: **Schaum's Outline of Electromagnetics, Fifth Edition

**Publisher: **McGraw-Hill Education: New York, Chicago, San Francisco, Athens, London, Madrid, Mexico City, Milan, New Delhi, Singapore, Sydney, Toronto

**Copyright / Pub. Date: **2019 McGraw-Hill Education

**ISBN: **9781260120974

**Authors:****Mahmood Nahvi**
is professor emeritus of electrical engineering at California Polytechnic State University (Cal Poly) in San Luis Obispo, California. He earned B.Sc., M.Sc., and Ph.D. degrees in electrical engineering, and has more than 55 years of educational, academic, research, and industrial experience in this field. He has taught undergraduate and graduate courses on various subjects including electric circuits, electronics, signals and systems, electromagnetics, random signals and noise, digital signal and image processing, and communications and control. Dr. Nahvi's areas of special interest and expertise include network theory, control theory, adaptation and learning in synthetic and living systems, communication and control in living systems, neural networks for pattern recognition and motor control, satellite communication, digital signal and image processing, and engineering education. In the area of engineering education, he has developed computer modules for electric circuits, signals, and systems that improve the teaching and learning of the fundamentals of electrical engineering. Dr. Nahvi is the author of Signals and Systems (McGraw-Hill, 2014). He is also the co-author, with Joseph A. Edminister, of Schaum's Outline of Electric Circuits.
**Joseph A. Edminister**
is professor emeritus of electrical engineering at the University of Akron in Akron, Ohio, where he also served as assistant dean and acting dean of engineering. He was a member or the faculty from 1957 until his retirement in 1983. In 1984 he served on the staff of Congressman Dennis Eckart of Ohio on an IEEE Congressional Fellowship. Professor Edminister then joined Cornell University as a patent attorney and later as director of corporate relations for the College of Engineering until his retirement in 1995. He received his B.S.E.E. in 1957, his M.S.E. in 1960, and his J.D. in 1974, all from the University of Akron. Professor Edminister is a registered professional engineer in Ohio, a member of the bar in Ohio, and a registered patent attorney.

**Description: **
Tough test questions? Missed lectures? Not enough time?
Fortunately, there's Schaum's.
More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.
This Schaum's Outline gives you:
• Hundreds of supplementary problems to reinforce knowledge
• Concise explanations of all electromagnetic concepts
• Information on current density, capacitance, magnetic fields, inductance, electromagnetic waves, transmission lines, and antennas
• New section on transmission line parameters
• New section illustrating the use of admittance plane and Smith Chart
• New section on impedance transformation
• New chapter on sky waves, attenuation and delay effects in troposphere, line-of-sight propagation, and other relevant topics
• Support for all major textbooks for courses in electromagnetics
PLUS: Access to revised Schaums.com website with 24 problem-solving videos, and more.
Schaum's reinforces the main concepts required in your course and offers hundreds of practice questions to help you succeed. Use Schaum's to shorten your study time and get your best test scores!