The divergence of a vector field is defined as
This is easily seen from the definition of the dot product and that of the del operator
carrying out the dot product with
then gives (1).
(this section is a work in progress)
Building physical intuition about the divergence of a vector field can be gained by considering the flow of a fluid. One of the most simple vector fields is a uniform velocity field shown in below figure.
Mathematically, this field would be
The divergence is then
Source/Sink flow field ( div > 0 / div < 0)
Circular flow with zero divergence
Cartesian Coordinates
Cylindrical Coordinates
Spherical Coordinates
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