Examples of divergence of a vector field? - Answers

I am not sure if this is the answer you are looking for, since the question is listed in both Physics and Abstract Algebra, so I will try to give you some examples from physics. One of the indicators of a divergence of a vector field is the presence of a source. For example the electric field can be represented by a vector field, with each vector pointing along the field and has a length proportional to the strength of the electric field at that position. A point source then causes an electric field with a divergence at the location of the point source, with the vectors all pointing away from it (positive charge) or towards it (negative charge). Another example would be some point mass and the Newtonian gravitational field. One of Maxwell's equations states that the magnetic field cannot have any divergences meaning that there are no magnetic monopoles.