Electromagnetic Field Theory
The wave in wave guide has

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

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Electromagnetic Field Theory
Gradient of scalar field is expressed as

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

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