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Divergence of a Vector

In vector calculus, the divergence is an operator that measures the magnitude of a vector field's source or sink at a given point; the divergence of a vector field is a (signed) scalar. For example, consider air as it is heated or cooled. The relevant vector field for this example is the velocity of the moving air at a point. If air is heated in a region it will expand in all directions such that the velocity field points outward from that region. Therefore the divergence of the velocity field in that region would have a positive value, as the region is a source. If the air cools and contracts, the divergence is negative and the region is called a sink. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point. - Wikipedia

 

 

"Ñ" is a vector and is pronounced "del." The vector function is A(x,y,z), A(r,Φ,z), or A(r,θ,Φ)

Cartesian Coordinates
Divergence of a Vector Cartesian Coordinates - RF Cafe
Cylindrical Coordinates
Divergence of a Vector Cylindrical Coordinates - RF Cafe
Spherical Coordinates
Divergence of a Vector Spherical Coordinates - RF Cafe