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

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1. May 6, 2017

### Zohaib_aarfi

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

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File size:
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2. May 7, 2017

### haushofer

What is correct probably depends on your conventions, which you don't give.

3. May 7, 2017

### vanhees71

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. May 8, 2017

### Zohaib_aarfi

Thank you for your response. I am using metric $$diag(1,-1)$$ and the expression you gave $$B^i = - \epsilon_{ijk} \partial_j A^k$$ contains also $$A^i = - A_i$$, so I think it does not make any difference. Could you do it for me in complete and explicit steps?