Skip to main content
Engineering LibreTexts

2.1: What is a Field?

  • Page ID
    3902
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

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

    Definition: Field

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

    In electromagnetics, the electric field intensity \(\mathbf{E}\) is a real-valued vector field that may vary as a function of position and time, and so might be indicated as “\(\mathbf{E}(x, y, z, t),”\) “\(\mathbf{E} ( \mathbf { r } , t )\),” or simply “\(\mathbf{E}\).” When expressed as a phasor, this quantity is complex-valued but exhibits no time dependence, so we might say instead “\(\widetilde { \mathbf { E } } ( \mathbf { r } )\)” or simply “\(\widetilde { \mathbf { E } }\).”

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

    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.


    This page titled 2.1: What is a Field? is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Steven W. Ellingson (Virginia Tech Libraries' Open Education Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.