- #1

Sunshine

- 31

- 0

[tex]\nabla \times \dfrac{\vec{A} \times \vec{r}}{2}[/tex]

solving normally isn't any problem, but I have to do it with index notation, where A is an arbitrary vector field and r is the position vector)

This is how far I can come:

(leaving out the vector-lines above A and r)

[tex]\frac{1}{4}(\nabla \times (A \times r)) = \frac{1}{4}\epsilon_{ijk}\cdot \partial_{j}(A \times r)_k = \frac{1}{4}\epsilon_{ijk}\cdot \partial_{j}(\epsilon_{klm} \cdot A_l \cdot r_m) = \frac{1}{4}\epsilon_{ijk} \epsilon_{klm}\cdot \partial_{j}(A_l \cdot r_m) = \frac{1}{4}\epsilon_{ijk} \epsilon_{klm}(r_m \cdot \partial_j A_l + A_l \cdot \partial_j r_m)[/tex]

But then what...? I'm not even sure I'm allowed to bring in that [tex]\epsilon_{klm}[/tex]. I'm very new to this notation, and don't know much more than einstein's summation convention.