# Book:I.S. Grant/Electromagnetism/Second Edition

## I.S. Grant and W.R. Phillips: Electromagnetism (2nd Edition)

Published $\text {1990}$, John Wiley & Sons, Ltd

ISBN 0-471-92712-0.

### Contents

Flow diagram
Preface to the Second Edition (January, 1990)
Preface to the First Edition (May, 1974)

$1$ FORCE AND ENERGY IN ELECTROSTATICS
$1.1$ Electric Charge
$1.2$ The Electric Field
$1.3$ Electric Fields in Matter
$1.3.1$ The Atomic Charge Density
$1.3.2$ The Atomic Electric Field
$1.3.3$ The Macroscopic Electric Field
$1.4$ Gauss' Law
$1.4.1$ The Flux of a Vector Field
$1.4.2$ The Flux of the Electric Field out of a Closed Surface
$1.4.3$ The Divergence of a Vector Field
$1.4.4$ The Differential Form of Gauss' Law
$1.5$ Electrostatic Energy
$1.5.1$ The Electrostatic Potential
$1.5.2$ The Electric Field as the Gradient of the Potential
$1.5.3$ The Dipole Potential
$1.5.4$ Energy Changes Associated with the Atomic Field
$1.5.5$ Capacitors, and Energy in Macroscopic Fields
$\star \ 1.5.6$ Energy Stored by a Number of Charged Conductors
Problems $1$

$\star$ Starred sections may be omitted as they are not required later in the book.

$2$ DIELECTRICS
$2.1$ Polarization
$2.2$ Relative Permittivity and Electric Susceptibility
$2.2.1$ The Local Field
$2.2.2$ Polar Molecules
$2.2.3$ Non-polar Liquids
$2.3$ Macroscopic Fields in Dielectrics
$2.3.1$ The Volume Density of Polarization Charge
$2.3.2$ The Electric Displacement Vector
$2.3.3$ Boundary Conditions for $\mathbf D$ and $\mathbf E$
$2.4$ Energy in the Presence of Dielectrics
$\star \ 2.4.1$ Some Further Remarks about Energy and Forces
Problems $2$

$3$ ELECTRIC FIELD CALCULATIONS
$3.1$ Poisson's Equation and Laplace's Equation
$3.1.1$ The Uniqueness Theorem
$3.1.2$ Electric Fields in the Presence of Free Charge
$3.2$ Boundaries Between Different Regions
$\star \ 3.3$ Boundary Conditions and Field Patterns
$\star \ 3.3.1$ Electrostatic Images
$\star \ 3.3.2$ Spheres and Spherical Cavities in Uniform External Field
$\star \ 3.4$ Electrostatic Lenses
$\star \ 3.5$ Numerical Solutions of Poisson's Equation
$3.6$ Summary of Electrostatics
Problems $3$

$4$ STEADY CURRENTS AND MAGNETIC FIELDS
$4.1$ Electromotive Force and Conduction
$4.1.1$ Current and Resistance
$\star \ 4.1.2$ The Calculation of Resistance
$4.2$ The Magnetic Field
$4.2.1$ The Lorentz Force
$4.2.2$ Magnetic Field Lines
$4.3$ The Magnetic Dipole
$4.3.1$ Current Loops in External Fields
$4.3.2$ Magnetic Dipoles and Magnetic Fields
$4.4$ Ampère's Law
$4.4.1$ The Field of a Large Current Loop
$4.4.2$ The Biot-Savart Law
$4.4.3$ Examples of the Calculation of Magnetic Fields
$4.5$ The Differential Form of Ampère's Law
$4.5.1$ The Operator Curl
$4.5.2$ The Vector Curl $\mathbf B$
$4.5.3$ The Magnetic Vector Potential
$4.6$ Forces and Torques on Coils
$4.6.1$ Magnetic Flux
$4.7$ The Motion of Charged Particles in Electric and Magnetic Fields
$4.7.1$ The Motion of a Charged Particle in a Uniform Magnetic Field
$4.7.2$ Magnetic Mirrors and Plasmas
$\star \ 4.7.3$ Magnetic Quadrupole Lenses
Problems $4$

$5$ MAGNETIC MATERIALS
$5.1$ Magnetization
$5.1.1$ Diamagnetism
$5.1.2$ Paramagnetism
$5.1.3$ Ferromagnetism
$5.2$ The Macroscopic Magnetic Field Inside Media
$5.2.1$ The Surface Currents on a Uniformly Magnetized Body
$5.2.2$ The Distributed Currents Within a Magnetized Body
$5.2.3$ Magnetic Susceptibility and Atomic Structure
$5.3$ The Field Vector $\mathbf H$
$5.3.1$ Ampère's Law for the Field $\mathbf H$
$5.3.2$ The Boundary Conditions on the Field $\mathbf B$ and $\mathbf H$
$5.4$ Magnets
$5.4.1$ Electromagnets
$\star \ 5.4.2$ Permanent Magnets
$5.5$ Summary of Magnetostatics
Problems $5$

$6$ ELECTROMAGNETIC INDUCTION AND MAGNETIC ENERGY
$6.1$ Electromagnetic Induction
$6.1.1$ Motional Electromotive Force
$6.1.2$ Faraday's Law
$6.1.3$ Examples of Induction
$6.1.4$ The Differential Form of Faraday's Law
$6.2$ Self-inductance and Mutual Inductance
$6.2.1$ Self-inductance
$6.2.2$ Mutual Inductance
$6.3$ Energy and Forces in Magnetic Fields
$6.3.1$ The Magnetic Energy Stored in an Inductor
$6.3.2$ The Total Magnetic Energy of a System of Currents
$6.3.3$ The Potential Energy of a Coil in a Field and the Force on the Coil
$6.3.4$ The Total Magnetic Energy in Terms of the Fields $\mathbf B$ and $\mathbf H$
$6.3.5$ Non-linear Media
$\star \ 6.3.6$ Further Comments on Energy in Magnetic Fields
$6.4$ The Measurement of Magnetic Fields and Susceptibilities
$6.4.1$ The Measurement of Magnetic Fields
$6.4.2$ The Measurement of Magnetic Susceptibilities
Problems $6$

$7$ ALTERNATING CURRENTS AND TRANSIENTS
$7.1$ Alternating Current Generators
$7.2$ Amplitude, Phase and Period
$7.3$ Resistance, Capacitance and Inductance in A.C. Circuits
$7.4$ The Phasor Diagram and Complex Impedance
$7.5$ Power in A.C. Circuits
$7.6$ Resonance
$7.7$ Transients
Problems $7$

$8$ LINEAR CIRUITS
$8.1$ Networks
$8.1.1$ Kirchhoff's Rules
$8.1.2$ Loop Analysis, Node Analysis and Superposition
$8.1.3$ A.C. Networks
$8.2$ Audio-frequency Bridges
$8.3$ Impedance and Admittance
$8.3.1$ Input Impedance
$8.3.2$ Output Impedance and Thévenin's Theorem
$8.4$ Filters
$8.4.1$ Ladder Networks
$8.4.2$ Higher Order Filter and Delay Lines
$8.5$ Transformers
$8.5.1$ The Ideal Transformer
$8.5.2$ Applications of Transformers
$\star \ 8.5.3$ Real Transformers
Problems $8$

$9$ TRANSMISSION LINES
$9.1$ Propagation of Signals in a Lossless Transmission Line
$9.2$ Practical Types of Transmission Line
$9.2.1$ The Parallel Wire Transmission Line
$9.2.2$ The Coaxial Cable
$9.2.3$ Parallel Strip Lines
$9.3$ Reflections
$\star \ 9.4$ The Input Impediance of a Mismatched Line
$\star \ 9.5$ Lossy Lines
Problems $9$

$10$ MAXWELL'S EQUATIONS
$10.1$ The Equation of Continuity
$10.2$ Displacement Current
$10.3$ Maxwell's Equations
$10.4$ Electromagnetic Radiation
$\star \ 10.5$ The Microscopic Field Equations
Problems $10$

$11$ ELECTROMAGNETIC WAVES
$11.1$ Electromagnetic Waves in Free Space
$11.2$ Plane Waves and Polarization
$11.2.1$ Plane Waves in Free Space
$11.2.2$ Plane Waves in Isotropic Insulating Media
$11.3$ Dispersion
$11.4$ Energy in Electromagnetic Waves
$11.5$ The Absorption of Plane Waves in Conductors and the Skin Effect
$11.6$ The Reflection and Transmission of Electromagnetic Waves
$11.6.1$ Boundary Conditions on Electric and Magnetic Fields
$11.6.2$ Reflection at Dielectric Boundaries
$11.6.3$ Reflection at Metallic Boundaries
$\star \ 11.6.4$ Polarization by Reflection
$\star \ 11.7$ Electromagnetic Waves and Photons
Problems $11$

$12$ WAVEGUIDES
$12.1$ The Propagation of Waves Between Conducting Plates
$12.2$ Rectangular Waveguides
$12.2.1$ The $\operatorname {TE}_{01}$ Mode
$\star \ 12.2.2$ Further Comments on Waveguides
$12.3$ Cavities
Problems $12$

$13$ THE GENERATION OF MAGNETIC WAVES
$13.1$ The Retarded Potentials
$13.2$ The Hertzian Dipole
$13.3$ Antennas
Problems $13$

$14$ ELECTROMAGNETISM AND SPECIAL RELATIVITY
$14.1$ Introductory Remarks
$14.2$ The Lorentz Transformation
$14.3$ Charges and Fields as seen by Different Observers
$14.4$ Four-vectors
$14.5$ Maxwell's Equations in Four-vector Form
$14.6$ Transformation of the Fields
$14.7$ Magnetism as a Relativistic Phenomenon
$14.8$ Retarded Potentials From the Relativistic Standpoint
Problems $14$

APPENDIX A UNITS
$\text A.1$ Electrical Units and Standards
$\text A.1.1$ The Definition of the Ampere
$\text A.1.2$ Calibration and Comparison of Electrical Standards
$\text A.2$ Gaussian Units
$\text A.3$ Conversion between SI and Gaussian Units

APPENDIX B FIELDS AND DIFFERENTIAL OPERATORS
$\text B.1$ The operators $\operatorname {div}$, $\grad$ and $\curl$
$\text B.2$ Formulae in Different Coordinate Systems
$\text B.3$ Identities

APPENDIX C THE DERIVATION OF THE BIOT-SAVART LAW
Solutions to Problems