<P> In vector calculus, divergence is a vector operator that produces a scalar field giving the quantity of a vector field's source at each point . More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point . </P> <P> As an example, consider air as it is heated or cooled . The velocity of the air at each point defines a vector field . While air is heated in a region, it expands in all directions, and thus the velocity field points outward from that region . The divergence of the velocity field in that region would thus have a positive value . While the air is cooled and thus contracting, the divergence of the velocity has a negative value . </P> <P> In physical terms, the divergence of a three - dimensional vector field is the extent to which the vector field flow behaves like a source at a given point . It is a local measure of its "outgoingness"--the extent to which there is more of some quantity exiting an infinitesimal region of space than entering it . If the divergence is nonzero at some point then there must be a source or sink at that position . (Note that we are imagining the vector field to be like the velocity vector field of a fluid (in motion) when we use the terms flow, source and so on .) </P> <P> More rigorously, the divergence of a vector field F at a point p can be defined as the limit of the net flow of F across the smooth boundary of a three - dimensional region V divided by the volume of V as V shrinks to p . Formally, </P>

What is the physical significance of divergence of a vector field
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