Everything about Divergence totally explained
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 a
vector field that denotes the
velocity of air expanding as it's heated, the divergence of the velocity field would have a positive value because the air expands. If the air cools and contracts, the divergence is negative. The divergence could be thought of as a measure of the change in density.
A vector field that has zero divergence everywhere is called
solenoidal.
Definition
Let
x, y, z be a system of
Cartesian coordinates on a 3-dimensional
Euclidean space, and let
i,
j,
k be the corresponding
basis of
unit vectors.
The divergence of a
continuously differentiable vector field F =
Fx i +
Fy j +
Fz k is defined to be the
scalar-valued function:
»
where the second expression is the contraction of the vectorfield valued 1 -form
with itself and the last expression is the traditional coordinate expression used by physicists.
Further Information
Get more info on 'Divergence'.
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