Electromagnetic Field Theory
Gradient of scalar field is expressed as

 Gradient of divergence of a vector field minus the curl of the vector field.
 Outward flux of a vector field per unit volume as the volume about the point tends to zero.
 Circulation of a vector field per unit area as the area tends to zero.
 Maximum rate of increase of scalar function at a point.

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Electromagnetic Field Theory
The wave in wave guide has

Larger wavelength than in the free space
Group velocity inversely proportional to wavelength
Diminishing wavelength than in the free space
Larger frequency than in the free space

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