**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

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