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I have some questions concerning the del operator when you use it together with the epsilon tensor and kronecker delta:

1. if you have:

phi - scalar, B vector fields

[tex]\partial_j(\phi B)_i[/tex]

is it equal to: [tex]\partial_j(\phi B)_i=(\partial_j\phi)B_i+\phi(\partial_jB_i)[/tex]

or I also have to index phi

2. How do I know if del represents rot or div of a vector field in a mixed expression? (ok, for the rot we also need the epsilon tensor, but there are some mixed identities where I can`t figure it out)

Here`s an example, maybe you could give me some advice on it:

[tex]div(\vec E\times \vec B)=\vec B. rot \vec E- \vec E. rot \vec B[/tex]

[tex]div(\vec E\times \vec B)=\partial_i(\vec E\times \vec B)_i=\partial_i\epsilon_{jki}E_j B_k=\epsilon_{ijk} \partial_i(E_j B_k)=\epsilon_{ijk} (\partial_i E_j)B_k + \epsilon_{ijk} E_j (\partial_i B_k)[/tex]

and now I don`t know how to express [tex](\partial_i B_k)[/tex] again in vectors

I would be glad I anyone could explain to me the entity of the operations and maybe give me some advice how to use them properly :)

thanks in advance, marin