- #1
Urmi Roy
- 753
- 1
I have some conceptual problems with divergence...
1.divergence is supposed to be the flux per unit volume at a particular point...again,I saw on wikipedia,that they define divergence as "the derivative of net flow of of the vector field across surface of a small region relative to the volume of the region...I can't see how these two defineitions are equivalent.
2. The word 'flow' is used in the above definition...all vectors however can't have 'flow',like the displacement vector for example...right?
3.I found on a website, an example illustrating divergence...it said, that for a particular vector field,the change of the vector along x axis,y axis and z axis were 1,-2,3...subsequently,the author calculated the divergence as 1-2+3=2...how can the divergence be obtained just like that? I don't understand.
4.As I said,the divergence is the volume density of flux...however,in the formulation of the divergence in terms of the del operator does not include 'volume' anywhere...please explain.
5. Again,the divergence is said to be a measure of the expansion of a vector field at a point,but the notion of divergence as "volume density of flux" does not seem to indicate any 'expansion'.
6. The point itself at which the divergence is being measured may not be a source or sink of flux...a vector might just be passing the point...right?
Sorry for asking so many questions! I need to get my head around this.
1.divergence is supposed to be the flux per unit volume at a particular point...again,I saw on wikipedia,that they define divergence as "the derivative of net flow of of the vector field across surface of a small region relative to the volume of the region...I can't see how these two defineitions are equivalent.
2. The word 'flow' is used in the above definition...all vectors however can't have 'flow',like the displacement vector for example...right?
3.I found on a website, an example illustrating divergence...it said, that for a particular vector field,the change of the vector along x axis,y axis and z axis were 1,-2,3...subsequently,the author calculated the divergence as 1-2+3=2...how can the divergence be obtained just like that? I don't understand.
4.As I said,the divergence is the volume density of flux...however,in the formulation of the divergence in terms of the del operator does not include 'volume' anywhere...please explain.
5. Again,the divergence is said to be a measure of the expansion of a vector field at a point,but the notion of divergence as "volume density of flux" does not seem to indicate any 'expansion'.
6. The point itself at which the divergence is being measured may not be a source or sink of flux...a vector might just be passing the point...right?
Sorry for asking so many questions! I need to get my head around this.