# 2.1: What is a Field?

Definition

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 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., $$\mathrm{V (r, t)}$$.

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