I What is the gradient of a divergence and is it always zero?

Hi Folks,

Was just curious as to what is the gradient of a divergence is and is it always equal to the zero vector. I am doing some free lance research and find that I need to refresh my knowledge of vector calculus a bit. I am having some difficulty with finding web-based sources for the gradient of a divergence.
 
Thanks for the info fresh_42. I found those two links very helpful and I solved my problem of the reason for my inquiry.
 

Charles Link

Homework Helper
Insights Author
Gold Member
2018 Award
4,390
1,862
One very important vector identity, (it is used in showing Maxwell's equations result in an electromagnetic wave equation), is ## \nabla \times \nabla \times \vec{A}=\nabla (\nabla \cdot \vec{A})-\nabla^2 \vec{A} ##. For the case that is often shown to demonstrate the wave equation in a vacuum, ## \nabla \cdot \vec{E}=0 ##, but in general, the first term on the right side of the vector identity equation is not equal to zero.
 

Want to reply to this thread?

"What is the gradient of a divergence and is it always zero?" You must log in or register to reply here.

Related Threads for: What is the gradient of a divergence and is it always zero?

Replies
1
Views
3K
  • Posted
Replies
1
Views
851
Replies
7
Views
14K
Replies
4
Views
4K
  • Posted
Replies
3
Views
4K
Replies
3
Views
694
Replies
8
Views
8K
  • Posted
Replies
3
Views
2K
Top