# 1: Preliminary Concepts

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A field is the continuum of values of a quantity as a function of position and time.

The quantity that the field describes may be a scalar or a vector, and the scalar part may be either real- or complex-valued.

In electromagnetics, the electric field intensity $${\bf E}$$ is a real-valued vector field that may vary as a function of position and time, and so might be indicated as “$${\bf E}(x,y,z,t)$$,” “$${\bf E}({\bf r},t)$$,” or simply “$${\bf E}$$.” When expressed as a phasor, this quantity is complex-valued but exhibits no time dependence, so we might say instead “$$\widetilde ParseError: invalid DekiScript (click for details) Callstack: at (Bookshelves/Electrical_Engineering/Book:_Electromagnetics_I_(Ellingson)/1:_Preliminary_Concepts), /content/body/p[4]/span[5]/span, line 1, column 1  ({\bf r})$$” or simply “$$\widetilde ParseError: invalid DekiScript (click for details) Callstack: at (Bookshelves/Electrical_Engineering/Book:_Electromagnetics_I_(Ellingson)/1:_Preliminary_Concepts), /content/body/p[4]/span[6]/span, line 1, column 1 $$
.”

An example of a scalar field in electromagnetics is the electric potential, $$V$$; i.e., $$V({\bf r},t)$$.

A wave is a time-varying field that continues to exist in the absence of the source that created it and is therefore able to transport energy.

• 1.1: What is Electromagnetics?
The topic of this book is applied engineering electromagnetics.
• 1.2: Electromagnetic Spectrum
Electromagnetic fields exist at frequencies from DC (0 Hz) to at least 1020 Hz – that’s at least 20 orders of magnitude!
• 1.3: Fundamentals of Waves
In this section, we formally introduce the concept of a wave and explain some basic characteristics.
• 1.4: Guided and Unguided Waves
Broadly speaking, waves may be either guided or unguided. Unguided waves include those that are radiated by antennas, as well as those that are unintentionally radiated. Once initiated, these waves propagate in an uncontrolled manner until they are redirected by scattering or dissipated by losses associated with materials.
• 1.5: Phasors
In many areas of engineering, signals are well-modeled as sinusoids. Also, devices that process these signals are often well-modeled as linear time-invariant (LTI) systems. The response of an LTI system to any linear combination of sinusoids is another linear combination of sinusoids having the same frequencies.
• 1.6: Units
The term “unit” refers to the measure used to express a physical quantity
• 1.7: Notation
The list below describes notation used in this book

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