2.1: What is a Field?

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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.

Contributors and Attributions

Ellingson, Steven W. (2018) Electromagnetics, Vol. 1. Blacksburg, VA: VT Publishing. https://doi.org/10.21061/electromagnetics-vol-1 Licensed with CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0. Report adoption of this book here. If you are a professor reviewing, adopting, or adapting this textbook please help us understand a little more about your use by filling out this form.