Electromagnetic Field Theory
A rectangular waveguide is a

Hollow rectangular conducting tube through which electromagnetic waves can be propagat-ed
Rectangular conducting wire to propagate electromagnetic waves
Tube antenna to transmit and receive electromagnetic waves
Hollow rectangular walled room carrying electromagnetic wave

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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.
 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.
 Maximum rate of increase of scalar function at a point.

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