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ELECTRO MAGNETIC THEORY
CONTENTS
Classica 1 electrodynamics
Electrostatics
Coulomb’s law
The electrostatic field
Magnetostatics
Ampère’s law
The magnetostatic field
Electrodynamics
Equation of continuity for electric charge
Maxwell’s displacement current
Electromotive force
Faraday’s law of induction
Maxwell’s microscopic equations
Maxwell’s microscopic equations
Electromagnetic duality
Bibliography
Examples
2 Electromagnetic wave
The wave equations
The wave equation for E
The wave equation for B
The time-independent wave equation for E
Plane waves
Telegrapher’s equation
Waves in conductive media
Observables and averages
Bibliography
Example
3 )Electromagnetic Potentials
The electrostatic scalar potential
The magnetostatic vector potential
The electrodynamic potentials
Gauge transformations
Gauge conditions
Lorenz-Lorentz gauge
Coulomb gauge
Velocity gauge
Bibliography
Examples
4) Electromagnetic Fields and Matter
Electric polarisation and displacement
Electric multipole moments
Magnetisation and the magnetising field
Energy and momentum
The energy theorem in Maxwell’s theory
The momentum theorem in Maxwell’s theory
Bibliography
Example
5) Electromagnetic Fields from Arbitrary Source Distributions
The magnetic field
The electric field
The radiation fields
Radiated energy
Monochromatic signals
Finite bandwidth signals
Bibliography
6) Electromagnetic Radiation and Radiating Systems
Radiation from an extended source volume at rest
Radiation from a two-dimensional current distribution
Radiation from a localised source volume at rest
The Hertz potential
Electric dipole radiation
Magnetic dipole radiation
Electric quadrupole radiation
Radiation from a localised charge in arbitrary motion
The Liénard-Wiechert potentials
Radiation from an accelerated point charge
Bremsstrahlung
Cyclotron and synchrotron radiation (magnetic bremsstrah
lung)
Radiation from charges moving in matter
Bibliography
Examples
7) Relativistic Electrodynamics
The special theory of relativity
The Lorentz transformation
Lorentz space
Minkowski space
Covariant classical mechanics
Covariant classical electrodynamics
The four-potential
The Liénard-Wiechert potentials
The electromagnetic field tensor
Bibliography
8) Electromagnetic Fields and Particles
Charged particles in an electromagnetic field
Covariant equations of motion
Covariant field theory
Lagrange-Hamilton formalism for fields and interactions
Bibliography
Example
Formulæ
The electromagnetic field
Maxwell’s equations
Fields and potentials
Force and energy
Electromagnetic radiation
Relationship between the field vectors in a plane wave
The far fields from an extended source distribution
The far fields from an electric dipole
The far fields from a magnetic dipole
The far fields from an electric quadrupole
The fields from a point charge in arbitrary motion
F3 Special relativity
Metric tensor
Covariant and contravariant four-vectors
Lorentz transformation of a four-vector
Invariant line element
Four-velocity
Four-momentum
Four-current density
Four-potential
Field tensor
Vector relations
Spherical polar coordinates
Vector formulae
Bibliography
Mathematical Methods
Scalars, vectors and tensors
Vectors
Fields
Vector algebra
Vector analysis
Analytical mechanics
Lagrange’s equations
Hamilton’s equations
Examples
Bibliography
Index