Correct relation is F^{ij} = - epsilon^{ijk} B^k.

  • #1

Main Question or Discussion Point

When I tried to derive this relation I got the wrong sign. Please check the pic and tell me my mistakes.
 

Attachments

Answers and Replies

  • #2
haushofer
Science Advisor
Insights Author
2,255
590
What is correct probably depends on your conventions, which you don't give.
 
  • #3
vanhees71
Science Advisor
Insights Author
Gold Member
2019 Award
13,813
5,621
If you use the west-coast convention you have ##\partial^l=-\partial_l##, and thus
$$B^i=-\epsilon_{ijk} \partial_j A^k.$$
Note that
$$\partial_j=\frac{\partial}{\partial x^j}.$$
 
  • #4
Thank you for your response. I am using metric [tex] diag(1,-1) [/tex] and the expression you gave [tex] B^i = - \epsilon_{ijk} \partial_j A^k [/tex] contains also [tex] A^i = - A_i [/tex], so I think it does not make any difference. Could you do it for me in complete and explicit steps?
 

Related Threads for: Correct relation is F^{ij} = - epsilon^{ijk} B^k.

  • Last Post
Replies
3
Views
658
Replies
0
Views
2K
  • Last Post
Replies
1
Views
134K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
127K
Replies
3
Views
685
Replies
7
Views
645
  • Last Post
Replies
6
Views
2K
Top