The goal of this chapter is to provide a summary of the basic concepts of electro- magnetic theory as a complement to the subject matter, most of which is related to electromagnetism, discussed in this book. The chapter covers only the concepts that are necessary to understand the electromagnetics of lightning flashes.

Chapter Contents:

• 1.1 Introduction
• 1.2 The nomenclature
• 1.3 Coordinate systems
• 1.4 Important vector relationships
• 1.4.1 The scalar product of two vectors
• 1.4.2 The vector product of two vectors
• 1.4.3 Vector field
• 1.4.4 The nabla operator and its operations
• 1.4.4.1 The gradient of a scalar function
• 1.4.4.2 The divergence of a vector field
• 1.4.4.3 The curl of a vector field
• 1.4.5 Important vector identities
• 1.4.6 Relationship between the curl of a vector field and the line integral of that vector field around a closed path
• 1.4.7 The flux of a vector field through a surface
• 1.4.8 Relationship between the divergence of a vector field and the flux of that vector field through a closed surface
• 1.4.9 Divergence theorem
• 1.4.10 Stokes theorem
• 1.5 Static electric fields
• 1.5.1 Coulomb's law
• 1.5.2 Electric field produced by static charges is a conservative field
• 1.5.3 Gauss's law
• 1.5.4 Electric scalar potential
• 1.5.5 Poisson and Laplace equations
• 1.5.6 Concept of images
• 1.5.7 Electrostatic boundary conditions
• 1.6 Static magnetic fields
• 1.6.1 Electric current
• 1.6.2 Conservation of electric charge
• 1.6.3 Re-distribution of excess charge placed inside a conducting body
• 1.6.4 Magnetic field produced by a current element - Biot-Savart's law
• 1.6.5 Gauss's law for magnetic fields
• 1.6.6 Ampere's law
• 1.6.7 Boundary conditions for the static magnetic field
• 1.6.8 Vector potential
• 1.6.8.1 Vector potential of a current distribution
• 1.6.8.2 Vector potential due to a current element dl
• 1.6.9 Force on a charged particle
• 1.7 Energy density of an electric field
• 1.8 Electrodynamics - Time-varying electric and magnetic fields
• 1.8.1 Faraday's law
• 1.8.2 Maxwell's modification of Ampere's law - the displacement current term
• 1.8.3 Energy density in a magnetic field
• 1.9 Summary of the laws of electricity
• 1.10 Wave equation
• 1.11 Maxwell's prediction of electromagnetic waves
• 1.12 Plane wave solution
• 1.12.1 The electric field of the plane wave
• 1.12.2 The magnetic field of the plane wave
• 1.12.3 Energy transported by a plane wave - Poynting's theorem
• 1.13 Maxwell's equations and plane waves in different media (summary)
• 1.13.1 Vacuum
• 1.13.2 Isotropic and linear dielectric and magnetic media
• 1.13.3 Conducting media
• 1.14 Retarded potentials
• 1.14.1 Vector potential of a current element
• 1.15 Electromagnetic fields of a current element - Electric dipole
• 1.16 Electromagnetic fields of a lightning return stroke
• Further reading

Inspec keywords: electromagnetism; lightning

Other keywords: electromagnetic theory; electromagnetism; lightning flash electromagnetics

Subjects: Classical electromagnetism; Atmospheric electricity