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2.1: What is a Field?

Last updated

Apr 2, 2020
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- 2: Electric and Magnetic Fields
- 2.2: Electric Field Intensity

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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.

Definition: Field

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