Electromagnetics Vol. 1 Study Guide and Chapter Summaries – Steven W. Ellingson (2018) BSEE/BS Physics

BS Electrical Engineering students taking their first course in electromagnetic field theory can get “Electromagnetics, Volume 1” free from Virginia Tech. It is a one-semester textbook by Steven W. Ellingson with 9 chapters and 3 appendices, written for third-year electrical engineering students. It uses a “transmission lines first” route: voltage and current waves on a cable come first, and the field laws follow in order as electrostatics, steady current, magnetostatics, time-varying fields and plane waves.

Starting from circuit ideas you already know makes the field theory easier to approach. Each short section builds one idea, and the text has 43 worked examples using real parts such as coaxial cable, circuit-board traces, transformers and generators. BS Physics students can use it as an engineering view of Maxwell’s equations. Volume 1 ends with uniform plane waves in lossless media; waveguides, optical fiber and antennas are in Volume 2, which is a separate book.

Book Overview

Chapter List

Chapter 1: Preliminary Concepts

Difficulty: Easy · Key topics: applied electromagnetics, electromagnetic spectrum, wavelength and wavenumber, phase velocity, guided and unguided waves, phasors, SI units, notation

The book opens by saying what it is for: closing the gap between lumped-element circuit theory and the field theory needed when materials and geometry matter, as in resistors that show reactance, antennas and circuit-board layout. It surveys the spectrum from DC to gamma rays, fixes the free-space speed at about 3.00 × 10⁸ m/s, and uses a sound-wave analogy to define wavenumber, wavelength and phase velocity. Guided waves (cables, waveguides, fiber) are separated from unguided ones radiated by antennas. The chapter closes with a primer on phasors, SI units and the notation used in later chapters.

Key Points:

• Free-space wavelength is λ = c/f: about 100 m at 3 MHz but only about 10 cm at 3 GHz, which is when a circuit’s size stops being negligible
• The radio band runs from about 3 kHz to 300 GHz; above it come infrared, optical, ultraviolet, X-rays and gamma rays
• A wave cos(ωt − βx) travels in the +x direction; β = 2π/λ is the wavenumber (phase propagation constant) and the phase velocity is v_p = ω/β = λf
• A phasor C = A_me^jψ stands for the sinusoid A(t) = Re{C e^jωt}
• Phasor analysis also covers narrowband signals and, through Fourier analysis, signals of any bandwidth
• The theory in this book is classical; quantum effects at X-ray frequencies and above are not covered

Memory Tip: With phasors, differentiating in time just means multiplying by jω. Put that rule on the first page of your notes, because it removes every time derivative in the chapters that follow.

Common Mistake: Treating a phasor as the signal itself. It is a complex constant that represents a sinusoid; to get the real waveform you multiply by e^jωt and take the real part.

Important Questions:

• What is the free-space wavelength of a 150 MHz signal? λ = c/f = (3 × 10⁸ m/s)/(150 × 10⁶ Hz) = 2 m.
• Why can phasor analysis be used for signals that are not pure sinusoids? Many signals are narrowband and behave like a sinusoid at their centre frequency. For any signal, Fourier analysis splits it into sinusoids, each is handled with phasors, and superposition adds the results.

Chapter 2: Electric and Magnetic Fields

Difficulty: Easy · Key topics: field, electric field intensity, permittivity, electric flux density, magnetic flux density, permeability, magnetic field intensity, constitutive parameters

This short chapter defines the field quantities used for the rest of the book. A field assigns a value to every point in space and time. Electric field intensity E is the force per unit test charge, and permittivity describes how a material changes the field a charge produces. Electric flux density D = εE is the same field described as flux. Magnetic flux density B is defined through the force on a moving charge, with permeability and magnetic field intensity H completing the set. The chapter ends with permittivity, permeability and conductivity as the three constitutive parameters, and the usual assumption of homogeneous, isotropic, linear, time-invariant material.

Key Points:

• E has units of V/m, and 1 V/m = 1 N/C; it points in the direction in which potential falls fastest
• Free-space permittivity is ε₀ ≈ 8.854 × 10⁻¹² F/m; relative permittivity ε_r = ε/ε₀ runs from 1 to about 60 in common engineering use
• D = εE has units of C/m², but it describes a field and is not itself a surface charge
• The magnetic force on a charge is F = qv × B: zero for a charge at rest, and perpendicular to both v and B; B is in tesla (Wb/m²)
• μ₀ = 4π × 10⁻⁷ H/m; μ_r is about 1 for most materials but can reach about 10⁶ in magnetic ones; H = B/μ in A/m
• The three constitutive parameters are ε, μ and conductivity σ (S/m); ideal media are homogeneous, isotropic, linear and time-invariant, which is what makes superposition work

Memory Tip: Pair the symbols: E goes with ε to give D, and H goes with μ to give B. The flux densities D and B are the ones you integrate over a surface, while E and H are the ones you integrate along a path.

Common Mistake: Reading D (units C/m²) as “the surface charge.” It is a description of the field, and it equals a real surface charge density only in special cases, such as at a conductor surface.

Important Questions:

• What is the electric field between two plates 2 mm apart with 5 V across them? E = V/d = 5 V / 0.002 m = 2500 V/m, pointing from the positive plate toward the negative one.
• Why does a magnetic field exert no force on a charge at rest? The force F = qv × B is proportional to the velocity, so it is zero when v = 0. A moving charge feels a force perpendicular to both its velocity and B.

Chapter 3: Transmission Lines

Difficulty: Hard · Key topics: TEM lines, lumped-element model, telegrapher’s equations, characteristic impedance, reflection coefficient, standing waves and SWR, input impedance, stubs, quarter-wave line, impedance matching

Transmission lines come first in this book. The chapter starts with why a cable stops being “transparent” once its length nears a wavelength, then separates TEM lines (coax, microstrip) from non-TEM ones (waveguide, multimode fiber). A lumped-element model with R′, L′, G′ and C′ per unit length leads to the telegrapher’s equations, the wave equation, the propagation constant and characteristic impedance. It then covers lossless lines, coax and microstrip design, the reflection coefficient, standing waves and SWR, input impedance, open and short stubs, quarter-wave sections, power flow, and matching with a single reactance or a single stub.

Key Points:

• Per-unit-length model: series R′ and L′, shunt G′ and C′; the propagation constant is γ = √[(R′ + jωL′)(G′ + jωC′)] = α + jβ
• Characteristic impedance Z₀ is the voltage-to-current ratio of a wave travelling one way; for a lossless line Z₀ = √(L′/C′) and v_p = 1/√(L′C′)
• Reflection coefficient Γ = (Z_L − Z₀)/(Z_L + Z₀): 0 for a matched load, +1 for an open circuit, −1 for a short; the current coefficient is −Γ
• SWR = (1 + |Γ|)/(1 − |Γ|), from 1 (matched) to infinity; a value below about 2 is usually a good match
• The input impedance of a terminated lossless line repeats every λ/2; a short stub gives jZ₀ tan(βl) and an open stub gives −jZ₀ cot(βl)
• A λ/4 line inverts impedance, and matching a real Z_L to a real source impedance Z_S needs a section with Z₀ = √(Z_SZ_L)
• The fraction of incident power that is reflected is |Γ|², so a modest mismatch wastes little power

Memory Tip: A quarter-wave line turns a short into an open and an open into a short, while a half-wave line gives back whatever load you put on it. Sketch these two cases and most stub questions answer themselves.

Common Mistake: Assuming the source sees the load impedance. Unless the line is matched (or an exact number of half-wavelengths long), the source sees the transformed input impedance, which depends on line length and frequency.

Important Questions:

• A 50 Ω line ends in a 150 Ω load. What are Γ and the SWR? Γ = (150 − 50)/(150 + 50) = 0.5, so SWR = 1.5/0.5 = 3. A quarter of the incident power (|Γ|² = 0.25) is reflected.
• How can a quarter-wave section match a 200 Ω load to a 50 Ω source? Make the section λ/4 long (in the line) with Z₀ = √(50 × 200) = 100 Ω. It only works directly when both impedances are real; a complex load needs a first line section to remove its imaginary part.

Chapter 4: Vector Analysis

Difficulty: Medium · Key topics: dot and cross product, Cartesian, cylindrical and spherical coordinates, line, surface and volume integrals, gradient, divergence, curl, Divergence Theorem, Stokes’ Theorem, Laplacian

This is the vector-mathematics toolkit the field equations need. It starts with vector arithmetic: position vectors, relative position, the dot product for angle and projection, and the cross product with the right-hand rule. It then sets out Cartesian, cylindrical and spherical coordinates with their basis vectors, differential lengths, areas and volumes, and shows how to integrate over curves, surfaces and volumes in each. The second half defines the differential operators by their physical meaning: gradient (direction of fastest increase), divergence (flux per unit volume) with its theorem, curl (circulation per unit area) with Stokes’ theorem, and the Laplacian.

Key Points:

• A · B = AB cos ψ is zero for perpendicular vectors; A × B has magnitude AB sin ψ, points by the right-hand rule, and changes sign if the order is swapped
• In cylindrical coordinates (ρ, φ, z) the length element along φ is ρdφ and dv = ρdρdφdz
• In spherical coordinates (r, θ, φ) dv = r² sin θ dr dθ dφ, and a sphere’s surface element is r² sin θ dθ dφ
• Cylindrical and spherical basis vectors change direction with position, so convert to Cartesian before adding vectors at different points
• The gradient ∇f points in the direction of steepest increase of f; it links field and potential through E = −∇V
• Divergence Theorem: the closed-surface integral of A equals the volume integral of ∇·A; Stokes’ Theorem: the closed-path integral of A equals the surface integral of ∇×A
• The Laplacian is ∇²f = ∇·(∇f); it links potential to charge density (Poisson) and appears in the wave equation

Memory Tip: For the Divergence Theorem, think “what is produced inside must leave through the skin.” For Stokes’ Theorem, think “the tiny swirls inside add up to the circulation around the edge.”

Common Mistake: Forgetting that φ and θ are angles, not lengths. The arc length is ρdφ (or r dθ), never just dφ.

Important Questions:

• How do you get the surface area of a sphere of radius a in spherical coordinates? Integrate the surface element: ∫ a² sin θ dθ dφ over θ from 0 to π and φ from 0 to 2π, which gives 4πa².
• What does Stokes’ Theorem say, and where is it used? The circulation of a vector field around a closed path equals the flux of its curl through any surface bounded by that path. The book uses it to turn the integral forms of Kirchhoff’s voltage law, Ampere’s law and Faraday’s law into differential equations.

Chapter 5: Electrostatics

Difficulty: Hard · Key topics: Coulomb’s law, charge distributions, Gauss’ law, electric potential, Poisson and Laplace equations, boundary conditions, conductors and dielectrics, capacitance, electrostatic energy

Electrostatics is the longest chapter. It starts from Coulomb’s law and the field of point charges, then extends to line, surface and volume charge distributions. Gauss’ law appears in integral form, used with symmetry as in the infinite line charge, and in differential form. Work, energy and potential difference lead to path independence, Kirchhoff’s voltage law for electrostatics, potentials of point and continuous charges, and E = −∇V. Poisson’s and Laplace’s equations are applied to a parallel-plate capacitor. After the boundary conditions on E and D, perfect conductors, dielectrics and breakdown, the chapter defines capacitance and electrostatic energy.

Key Points:

• A point charge q produces E = q/(4πεR²) pointing away from it; for several charges the fields add (superposition)
• Gauss’ law: the closed-surface integral of D equals the enclosed charge, and ∇·D = ρ_v at a point
• The potential difference between two points is independent of the path, so the integral of E around any closed path is zero and ∇×E = 0 in electrostatics
• A point charge has potential V = q/(4πεR) with the datum at infinity, and E = −∇V
• In a charge-free region the potential satisfies Laplace’s equation ∇²V = 0; with charge it is Poisson’s equation ∇²V = −ρ_v/ε
• At a boundary the tangential E is continuous and the normal D jumps by the surface charge; at a perfect conductor E_tan = 0 and D_normal = ρ_s
• Capacitance is C = Q/V: C = εA/d for a thin parallel-plate capacitor and C = 2πεl/ln(b/a) for a coaxial one; stored energy is ½CV², an energy density of ½εE²

Memory Tip: Choose your tool by the problem. Use the Coulomb integral for awkward shapes, Gauss’ law when the symmetry is planar, cylindrical or spherical, and Laplace’s equation when the boundaries (such as conducting plates) are what you know.

Common Mistake: Reaching for Gauss’ law on a charge distribution with no symmetry. The law is always true, but it only lets you solve for E when the symmetry makes E constant over the chosen surface.

Important Questions:

• A thin parallel-plate capacitor has plates of area 1 cm², a spacing of 1 mm and a spacer with ε_r = 4.5. What is its capacitance? C = εA/d = (4.5 × 8.854 × 10⁻¹² F/m)(10⁻⁴ m²)/(10⁻³ m) ≈ 4.0 pF, ignoring the fringing field.
• Why is the tangential electric field zero at the surface of a perfect conductor? The field inside is zero and the surface is at constant potential. The integral of E around a thin loop straddling the surface must vanish, so the tangential component just outside must be zero and E points straight out of the surface.

Chapter 6: Steady Current and Conductivity

Difficulty: Medium · Key topics: convection and conduction current, current density, conductivity, Ohm’s law at a point, resistance, conductance, power dissipation

This short chapter links the field picture to circuit resistance. It separates convection current (charge carried by moving matter) from conduction current (charge moving through a material under an electric field), and replaces the scalar circuit current with current density J, where the net current is the flux of J through a surface. Conductivity gives the point form of Ohm’s law and sorts materials from insulators to perfect conductors. The chapter then derives the resistance of a uniform wire, notes why resistance rises with frequency, defines conductance using a coaxial structure with a lossy spacer, and shows that dissipated power is the volume integral of E · J.

Key Points:

• Conduction current is driven by E inside a material; convection current is charge carried along by moving matter
• Volume current density J has units of A/m² and I = ∫J · ds; surface current density J_s is in A/m
• Ohm’s law at a point is J = σE, with conductivity σ in siemens per metre (S/m)
• A perfect conductor (σ → ∞) has E = 0 inside, so its potential is constant
• A uniform wire has R = l/(σA); at high frequency the current crowds toward the surface, the effective area shrinks and R increases
• Conductance G = 1/R is the more convenient quantity for leakage between the conductors of a coax
• Power dissipated as heat is P = ∫E · J dv, which reduces to I²R for a simple wire

Memory Tip: Resistance is “long over wide”: R = l/(σA). Double the length and R doubles; double the cross-section and R halves.

Common Mistake: Treating resistance as a property of the material. Conductivity is the material property; resistance also depends on the shape of the device and, at high frequency, on how the current spreads through it.

Important Questions:

• What is the resistance of 10 m of copper wire (σ = 5.8 × 10⁷ S/m) with a cross-section of 1 mm²? R = l/(σA) = 10/(5.8 × 10⁷ × 10⁻⁶) ≈ 0.17 Ω.
• Why is the electric field zero inside a perfect conductor? Since E = J/σ, letting σ grow without limit drives E to zero for any finite current density, so there can be no potential difference across the material.

Chapter 7: Magnetostatics

Difficulty: Hard · Key topics: Gauss’ law for magnetism, Ampere’s circuital law, wire, solenoid and toroid fields, boundary conditions, inductance, magnetic energy, magnetic materials

Magnetostatics is introduced by comparison with electrostatics, because many of the equations are duals of each other. Gauss’ law for magnetism (no net flux through a closed surface) and Ampere’s circuital law (circulation of H equals the enclosed current) are given in integral and differential form. Ampere’s law is then applied to an infinitely long wire, a straight coil, a toroidal coil and an infinite current sheet. Boundary conditions on B and H follow, then inductance in general and for a straight coil and a coaxial line, magnetic energy, and magnetic materials, from weak paramagnetic and diamagnetic media to ferromagnets with saturation and hysteresis.

Key Points:

• Gauss’ law for magnetism: the closed-surface integral of B is zero and ∇·B = 0, so magnetic field lines always close on themselves
• Ampere’s circuital law: the closed-path integral of H equals the enclosed current; in differential form ∇×H = J
• An infinitely long straight wire gives H = I/(2πρ), circling the wire by the right-hand rule
• Inside a long straight coil H ≈ NI/l and is nearly uniform; inside a toroid H = NI/(2πρ) and outside it is zero
• The normal component of B is continuous across a boundary, while the tangential H changes by any surface current J_s
• Inductance is L = NΦ/I and depends on geometry and μ; a long coil has L ≈ μN²A/l, and the stored energy is ½LI²
• Ferromagnetic materials (iron, nickel, cobalt) have very large μ_r but are nonlinear, showing saturation and hysteresis, which is what makes magnetic data storage possible

Memory Tip: Right-hand rule for Ampere’s law: point your thumb along the current and your fingers curl the way H circulates. For a coil, curl your fingers along the winding and your thumb gives the direction of the field inside.

Common Mistake: Thinking inductance depends on the current. In a linear material it depends only on geometry and permeability; the current just decides how much flux and energy there is.

Important Questions:

• How strong is H at 5 cm from a long straight wire carrying 10 A? H = I/(2πρ) = 10/(2π × 0.05) ≈ 32 A/m, directed around the wire.
• Why is the divergence of B always zero? No isolated magnetic charges exist, so every field line that leaves a region must return. The net magnetic flux through any closed surface is therefore zero.

Chapter 8: Time-Varying Fields

Difficulty: Medium · Key topics: Lenz’s law, Faraday’s law, transformer and motional emf, transformers, generators, Maxwell-Faraday equation, displacement current

This chapter shows what changes when fields vary in time. Lenz’s law gives the direction of induced effects: the induced field opposes the change. Faraday’s law gives the size, as an induced potential rather than a current, and the chapter separates transformer emf (changing B) from motional emf (a moving or rotating loop). These ideas are applied to a motionless loop, to transformers (voltage ratio, impedance scaling, why they block DC) and to a rudimentary generator. The static laws are then generalized: the Maxwell-Faraday equation replaces KVL, and Ampere’s law gains the displacement current term, which couples E and H.

Key Points:

• Lenz’s law: the current induced by a changing impressed field creates a field that opposes the change
• Faraday’s law: V = −N dΦ/dt, where Φ is the flux through any surface bounded by the loop; what is induced is a potential (emf) and the current then follows from Ohm’s law
• Transformer emf comes from a time-varying B; motional emf comes from a loop that moves, rotates or changes shape, which is how generators work
• An ideal transformer has V₁/V₂ = ±N₁/N₂, and impedance is scaled by (N₁/N₂)²
• Transformers do not pass DC (the flux must change) and saturate at very low frequency, so they act as high-pass devices, useful for isolation and for baluns
• Maxwell-Faraday equation: the closed-path integral of E equals −dΦ/dt, or ∇×E = −∂B/∂t
• With displacement current, Ampere’s law becomes ∇×H = J + ∂D/∂t, so a changing E also produces H

Memory Tip: Lenz’s law is nature’s negative feedback: whatever you do to the flux, the loop pushes back. If the induced field reinforced the change you would get energy from nothing, which conservation of energy forbids.

Common Mistake: Believing that induction depends on B itself rather than on how fast the flux changes. A constant B through a fixed loop induces nothing, and when a sinusoidal B passes through zero the induced voltage is at its maximum.

Important Questions:

• A transformer has 1000 primary and 100 secondary turns, wound in the same sense. With 230 V on the primary and a 10 Ω load, what are the secondary voltage and the impedance seen by the source? V₂ = 230 × 100/1000 = 23 V, and the source sees (1000/100)² × 10 Ω = 1000 Ω.
• Why was displacement current added to Ampere’s law? The original law fails where charge builds up with no conduction current, such as between capacitor plates. The ∂D/∂t term repairs this and lets a changing electric field create a magnetic field, which is what allows waves to exist.

Chapter 9: Plane Waves in Lossless Media

Difficulty: Hard · Key topics: Maxwell’s equations in phasor form, wave equation, spherical, cylindrical and plane waves, uniform plane waves, wave impedance, phase velocity, polarization, power density

The final chapter turns Maxwell’s equations into waves. It rewrites the four equations in phasor form, with time derivatives replaced by jω, then reduces them to vector wave equations for source-free, lossless, homogeneous regions. Spherical, cylindrical and plane waves are compared by the shape of their phasefronts, and the uniform plane wave is derived: E and H lie in the plane, are perpendicular to each other and to the direction of travel, and are related by the wave impedance. Phase velocity and wavelength follow, then linear, circular and elliptical polarization, and finally the time-average power density of a plane wave.

Key Points:

• In phasor form ∇×E = −jωB and ∇×H = J + jωD, so only spatial derivatives remain
• In a lossless, source-free region each field obeys ∇²E + β²E = 0 with β = ω√(με), the same β as in transmission-line theory
• A uniform plane wave travelling along +z has E = E₀e^−jβz pointing along x and H = (E₀/η)e^−jβz pointing along y; E, H and the direction of travel are mutually perpendicular
• Wave impedance is η = √(μ/ε), which is about 376.7 Ω in free space
• Phase velocity is v_p = 1/√(με) = c/√(μ_rε_r) and λ = v_p/f, so wavelength is shorter in any material than in free space
• Polarization may be linear, circular (equal amplitudes with a 90-degree phase shift, left or right) or elliptical; GPS satellites use circular polarization
• The time-average power density is S = |E₀|²/(2η) in W/m² for a peak amplitude E₀

Memory Tip: E cross H points the way the wave travels. Curl the fingers of your right hand from E toward H and your thumb shows the direction of propagation.

Common Mistake: Mixing peak and rms amplitudes. The formula S = |E₀|²/(2η) uses the peak value; with an rms field the factor of 2 disappears.

Important Questions:

• A uniform plane wave in free space has a peak electric field of 1 V/m. What is its time-average power density? S = E₀²/(2η₀) = 1/(2 × 376.7) ≈ 1.3 mW/m².
• What are the phase velocity and wavelength of a 1 GHz wave in a dielectric with ε_r = 4 and μ_r = 1? v_p = c/√4 = 1.5 × 10⁸ m/s, so λ = v_p/f = 15 cm, half the free-space wavelength of 30 cm.

Appendices A–C: Material Parameters, Mathematical Formulas and Constants

Appendix · Difficulty: Easy · Key topics: permittivity, permeability and conductivity of common materials, trigonometric identities, vector operators in three coordinate systems, vector identities, physical constants

Three short reference appendices close the book. Appendix A gives representative values of relative permittivity, relative permeability and conductivity for materials engineers meet every day, with notes on how these change with frequency and temperature. Appendix B collects trigonometric identities, the gradient, divergence, curl and Laplacian written out in Cartesian, cylindrical and spherical coordinates, and a list of vector identities. Appendix C lists the physical constants used in the text: the speed of light, the electron charge, the permittivity and permeability of free space, and the wave impedance of free space.

Key Points:

• Relative permittivity: about 1 for air, about 2.1 for Teflon, about 4.5 for FR4 circuit-board material, and roughly 72–81 for water
• Most materials have μ_r close to 1; electrical steel is about 4000 and ferrites range from about 16 to 640
• Conductivity: copper about 5.8 × 10⁷ S/m, seawater up to about 5 S/m, and good insulators below 10⁻¹⁵ S/m
• Constants: c ≈ 2.9979 × 10⁸ m/s, ε₀ ≈ 8.854 × 10⁻¹² F/m, μ₀ = 4π × 10⁻⁷ H/m, η₀ ≈ 376.7 Ω
• Appendix B is the page to keep open while working through Chapters 4 to 9

Memory Tip: Remember three anchor values for ε_r: about 1 for air, about 4.5 for FR4 board, and about 80 for water. They let you sanity-check a wavelength or a capacitance in seconds.

Common Mistake: Treating a table value as exact. Permittivity and conductivity change with frequency and temperature, and the book advises primary references when you need better than about 10 percent accuracy.

Important Questions:

• What is a typical relative permittivity for FR4, and why does it matter? About 4.5. It sets the capacitance of a printed-circuit structure and the speed and wavelength of waves on a microstrip line, so it decides the trace width for a 50 Ω line.
• Which materials have a relative permeability far above 1? Ferromagnetic ones: iron, electrical steel, nickel, cobalt and ferrites. Almost every other material has μ_r very close to 1.

How to Study This Book

The book is built for one semester and teaches in a fixed order: transmission lines (Chapter 3), then electrostatics (5), steady current (6), magnetostatics (7), time-varying fields (8) and plane waves (9). Chapters 1, 2 and 4 are preparation. Chapter 1 refreshes waves and phasors and Chapter 4 refreshes vector calculus, so skim them if your course has already covered those topics, and come back to Chapter 4 whenever a divergence, curl or coordinate system trips you up.

Chapter 3 is the biggest hurdle: it has 23 sections and several matching designs. Start with 3.4 to 3.8 (the lumped model, the telegrapher’s equations, characteristic impedance and wave propagation), because everything after depends on them. Then learn the reflection coefficient (3.12), standing waves and SWR (3.13 and 3.14), input impedance (3.15) and stubs (3.16 and 3.17). Sections 3.10 and 3.11 quote capacitance and inductance formulas for coax that are only derived later, in 5.24 and 7.14, so accept them on a first read and return after those chapters.

Work Chapters 5 and 7 side by side. The book itself points out that electrostatics and magnetostatics are duals (see the comparison table in 7.1), so each result in Chapter 7 echoes one in Chapter 5: Gauss’ law for D and for B, KVL for E and Ampere’s law for H, capacitance and inductance, electric and magnetic energy. The boundary-condition sections (5.17, 5.18, 7.10 and 7.11) are favourite exam topics, so learn which components are continuous and which jump.

Chapter 6 is short and mostly familiar, but keep 6.3 to 6.6 for the field view of resistance, conductance and Joule heating. Chapter 8 is where the static laws become Maxwell’s equations; read 8.2 and 8.3 first for the induction logic, then jump to 8.8 and 8.9, which are the two generalized laws that Chapter 9 depends on. Chapter 9 then rewards you with simple results: read 9.4 (derivation) once for the logic and spend your practice time on 9.5 to 9.7 (wavelength, polarization and power density).

Every section is written to stand alone, so you will notice some deliberate repetition of earlier material. The text also cites Wikipedia pages as optional reading for extra background. The book is classical electromagnetics only: quantum effects at X-ray and higher frequencies are not covered, and the Smith chart is mentioned only through further reading, with matching problems solved by numerical search.

Know what this volume leaves out. It stops at uniform plane waves in lossless media. Waves in lossy materials, reflection and transmission at boundaries, waveguides, optical fiber, radiation and antennas belong to Volume 2, which is a separate book by the same author. The PDF itself has worked examples (43 of them) but no end-of-chapter problems, so use the problem sets and solutions posted on the official VTechWorks page, or make your own practice from the examples.

Used In These Programs

This book is used for the Electromagnetic Field Theory course in: BS Electrical Engineering · BS Physics. Browse all Electromagnetics books or all Engineering books.

Who Should Read This

This book is written for BS Electrical Engineering students in their third year who are taking a first course in electromagnetic field theory, and it assumes you know circuits, linear systems, complex numbers, vectors, partial differential equations and multivariable calculus. If your vector calculus feels rusty, Calculus Volume 3 covers line and surface integrals, divergence and curl in more detail than Chapter 4 can. BS Physics students will find the field laws they know, but presented with an engineering eye on cables, circuit boards, transformers and antennas, and with no quantum or relativistic treatment; for the physics-first route start with University Physics Volume 2, which covers electricity and magnetism with a gentler pace. It is not the right book if you need antennas, waveguides or reflection at boundaries, which are in Volume 2 of this series. The chapters on transmission lines (3) and plane waves (9) are also useful revision for electrical engineering entry tests and interviews in RF and communications.

Applicable Universities

This book is useful for students at Pakistani universities offering BS Electrical Engineering or BS Physics including UET Lahore, NUST, COMSATS, FAST, GIKI, Punjab University, NED, and other HEC-recognized institutions, wherever a one-semester electromagnetics or electromagnetic field theory course is part of the degree.

Official Copy of Electromagnetics Vol. 1

This book is free from its official home, VTechWorks, the Virginia Tech repository. Click the button below to open the official page, where you can download the PDF and find the errata, slides, and problem sets with solutions.

FAQs

Related Books

• University Physics Volume 2 – OpenStax (electricity, magnetism and electromagnetic waves at a gentler pace)
• Calculus Volume 3 – OpenStax (line and surface integrals, divergence and curl)
• College Physics 2e – OpenStax (a first look at electric and magnetic fields)
• University Physics Volume 3 – OpenStax (light as an electromagnetic wave: interference, diffraction, relativity)

Electromagnetics, Volume 1 gives electrical engineering students a free, clear route from transmission lines through static and time-varying fields to plane waves, with worked examples drawn from real cables, circuit boards, transformers and generators. Browse more Engineering books or Physics books for the rest of your semester.

Electromagnetics, Volume 1, by Steven W. Ellingson. VT Publishing (Virginia Tech University Libraries), Blacksburg, Virginia, 2018. Licensed under the Creative Commons Attribution-ShareAlike 4.0 licence (CC BY-SA 4.0). DOI: https://doi.org/10.21061/electromagnetics-vol-1. Official page: https://vtechworks.lib.vt.edu/handle/10919/84164