I can do this derivation the old fashioned way, but am having trouble doing it with einstein summation notation.(adsbygoogle = window.adsbygoogle || []).push({});

Since [itex]\vec{B}=\nabla \times \vec{a}[/itex]

[itex]\vec{B}=\mu_{0}/4\pi (\nabla \times (m \times r)r^{-3}))[/itex]

[itex]4\pi \vec{B}/\mu_{0}=\epsilon_{ijk} \nabla_{j}(\epsilon_{klm} m_{l} r_{m} r^{-3})[/itex]

[itex]=(\delta_{il}\delta_{jm}-\delta_{im}\delta_{jl})\partial_{j}m_{l}r_{m}r^{-3}[/itex]

here is where I am stumbling. My professor has for the next step

[itex]=m_{l}(\delta_{il}\delta_{jm}-\delta_{im}\delta_{jl})r^{-3} \delta_{jm}-3 r_{m}\hat{r}_{j}r^{-4})[/itex]

but I don't really know how to get to that step

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# Einstein summation notation for magnetic dipole field

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