# Vector field, source of a

A point of the vector field $\mathbf a$ with the property that the flow of the field through any sufficiently small closed surface $\partial V$ enclosing it is independent of the surface and positive. The flow

$$Q = {\int\limits \int\limits } _ {\partial V } ( \mathbf n , \mathbf a ) d s ,$$

where $\mathbf n$ is the outward unit normal to $\partial V$ and $s$ is the area element of $\partial V$, is called the power of the source. If $Q$ is negative, one speaks of a sink. If the sources are continuously distributed over the domain $V$ considered, then the limit

$$\lim\limits _ {\partial V \rightarrow M } \ \frac{\int\limits \int\limits _ {\partial V } ( \mathbf a , \mathbf n ) d s }{V}$$

is called the density (intensity) of the source at the point $M$. It is equal to the divergence of $\mathbf a$ at $M$.