Patata#

Definición#

The divergence is an operator that is applied on a vector field.

(312)#\[\vec{\nabla}\cdot \vec{f}=\frac{\partial f_x}{\partial x}+\frac{\partial f_y}{\partial y}+\frac{\partial f_z}{\partial z}\]

As can be seen, the result of the applying the divergence is a scalar field.

Interpretation#

The divergence measures the difference between the number of field lines that enter and leave from/to a particular point.

Ejemplo

../_images/divergencia.png

Fig. 200 The divergence measures the number of lines entering/exiting a point.#

A positive divergence is associated with a majority of lines coming out (leaving) from a point. This point is a source of field lines. On the other hand, a point with a negative divergence is seen to come from a majority of lines entering into a point. This point is called a sink of field line.

Problems and solution examples#