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.