Kroneker delta

  • #1

Homework Statement


I need to prove B.(Gradient . B) - B X(Gradient X B)=Del{i} [B{i}B{j} -1/2 (kroneker delta {ij} B^2]

where I have used . as the dot product, {} as subscript. Thank you!

Homework Equations




The Attempt at a Solution


[/B]
I have attempted the solution but am not sure how it is possible to keep a kroneker delta on the right hand side.
 
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Answers and Replies

  • #2
Charles Link
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I can not read your complete statement above, but this looks like it comes from a standard vector identity: (where ## A ## and ## B ## are both equal to ## B ##).
## \nabla (A \cdot B)=(A \cdot \nabla) B +(B \cdot \nabla) A+A \times \nabla \times B+B \times \nabla \times A ##
 
  • #3
I have uploaded the page from Jackson it is equation (6.119) I am trying to prove, however I must use Levi Cevita notation.
 

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  • #4
Charles Link
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I have uploaded the page from Jackson it is equation (6.119) I am trying to prove, however I must use Levi Cevita notation.
On the left side of the equation in your OP, they are only taking one component. You may be able to use the identity I presented to simplify the ## B \times \nabla \times B ## term.
 

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