ROTACIONAL Y DIVERGENCIA DE UN CAMPO VECTORIAL

Always we give concepts but at this case always it is good to make relation with ejeplos relate probably little mas to the topic and to take it to some kind of(some) familiar(family) mas. Consequently, it is named a field to any mathematical object that is defined for any point of the space. In physics a magnitude is a field when it is defined in the whole space. If this magnitude is a number, one to climb, we will have a field climb, if it is on the other hand a vector, it will be a vectorial field.
For example, in one day with a lot of wind, the temperature that it(he,she) does in any part(report) of a city will be a field to climb. This way we can say that in the "such" point so many degrees of temperature exist and in "which(whom)" other certain degrees of temperature. In view of any point of the city saying that temperature does we will have a field climb (of temperatures). If for the same city we take the intensity and wind direction as a vector we will have a vectorial field. Analogous we will be able to say: In this point the vector of the speed of the wind is so much, but in this another point it(he,she) is. We will have a certain vectorial magnitude definite in all the points of the space.

I wait and my contribution has been pleasant to the forum and for it in the evening despues I explain to him(her) seño that this very well and good nights

Good night,

1. Divergence of a vector field.

We define the divergence of a vector field as:



The Ostrogradski-Gauss theorem tells us that the integral of the divergence of a vector field in a volume equal to the field flux through the surface bounding that volume, ie



2. Curl of a vector field.

We define the curl of a vector field as:



Stokes' theorem tells us that the circulation of a vector field along a closed line bordering a surface equals the flow of the curl of the vector field through that surface, ie

I want to expand the concept of vector fields with the following consideration


The vector fields are usually represented graphically by lines of force, indicating the direction and the direction of the field at each point. To complete this qualitative and quantitative have an idea about them, is taken as agreement that the density of field lines, ie their number per unit area, coincides with the field magnitude at each point. Then the physical meaning of the flux through a surface from a field is none other than the number of field lines of force crossing the surface, and the mean divergence, as positive or negative, the number of lines of force born or die in the unit volume. In field theory, the points are born or die where the field lines are called sources and sinks respectively, thus the divergence is the volume density of sources or sinks.