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

In summary, the conversation discusses the derivation of a relation and the sign discrepancy that occurred. It is mentioned that the correct answer may depend on conventions, specifically the west-coast convention where ##\partial^l = -\partial_l##. The final expression for ##B^i## is provided, taking into account the use of the metric diag(1,-1). The speaker then requests for a complete and explicit explanation of the process.
  • #1
Zohaib_aarfi
2
0
When I tried to derive this relation I got the wrong sign. Please check the pic and tell me my mistakes.
 

Attachments

  • 20170506_174023.jpg
    20170506_174023.jpg
    23.7 KB · Views: 413
  • 20170506_174023.jpg
    20170506_174023.jpg
    23.7 KB · Views: 433
Physics news on Phys.org
  • #2
What is correct probably depends on your conventions, which you don't give.
 
  • #3
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 to Correct relation is F^{ij} = - epsilon^{ijk} B^k.

1. What is the correct relation between F^{ij} and B^k?

The correct relation is given by F^{ij} = - epsilon^{ijk} B^k, where F^{ij} is the electromagnetic field tensor and B^k is the magnetic induction vector.

2. What does the epsilon^{ijk} term represent in the equation?

The epsilon^{ijk} term is the Levi-Civita symbol, which is used to represent the permutation of indices in three-dimensional space. It is equal to 1 if the indices are in ascending order, -1 if they are in descending order, and 0 if any two indices are equal.

3. How is this equation derived?

This equation is derived from Maxwell's equations, specifically the Faraday's law of induction and the Ampere's law. It is a mathematical representation of the relationship between the electromagnetic field and magnetic induction in three-dimensional space.

4. What are the physical implications of this equation?

This equation shows that the magnetic field is perpendicular to the electric field and that their strengths are directly proportional to each other. It also demonstrates the concept of electromagnetic waves and the propagation of energy through space.

5. Can this equation be applied in other contexts?

Yes, this equation can be applied in various contexts, such as in the study of electromagnetism, quantum mechanics, and relativity. It is also used in engineering and technology to understand and design electrical and electronic systems.

Similar threads

A Triangulating Hamiltonian Constraint in LQG
Replies
1
Views
801
Evaluating partition function (stuck for weeks)
Replies
3
Views
1K
Deriving Casimir operator from the Lie Algebra of the Lorentz Group
Replies
5
Views
2K
On the order of indices of the Christoffel symbol of the 1st kind
Replies
19
Views
598
Two equations "combined" don't give the desired result
Replies
3
Views
469
I Principle of relativity and Galileo's group
Replies
10
Views
1K
Elastic potential energy - different methods, different results
Replies
2
Views
370
B Non-physicist needs your help torquing a nut!
Replies
9
Views
617
B Another special relativity related "paradox"
Replies
15
Views
1K
I Types of symmetries in Lagrangian mechanics
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top