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.
A field is the continuum of values of a quantity as a function of position and time.
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 “E(x,y,z,t),” “E(r,t),” or simply “E.” When expressed as a phasor, this quantity is complex-valued but exhibits no time dependence, so we might say instead “˜E(r)” or simply “˜E.”
An example of a scalar field in electromagnetics is the electric potential, V; i.e., 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.