# Einstein-Notation: rot(rot(A))

1. Feb 20, 2013

### smoking-frog

1. The problem statement, all variables and given/known data
Write $$\nabla \times (\nabla \times \vec A)$$ in Einstein-Notation, whereas $$\vec A$$ is the vector potential of the magnetic field.

2. Relevant equations
$$(\vec a \times \vec b)=\varepsilon_{ijk} a_j b_k$$

3. The attempt at a solution
$$\nabla \times (\nabla \times \vec A)=\varepsilon_{ijk} \partial_j(\varepsilon_{lmn}\partial_m A_n)_k$$

What to do with $$(\varepsilon_{lmn}\partial_m A_n)_k$$ though?

2. Feb 20, 2013

### CompuChip

On the right hand side, there is summation over j and k, but i is a free index which only occurs once. What you really meant to write, then, is

$$(\vec a \times \vec b)_i=\varepsilon_{ijk} a_j b_k$$

3. Feb 21, 2013