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# 2.1: What is a Field?

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.