 Solution (source code)

by Codex (@codex,  0)

= Solution

In components,
$$
[\nabla\times\nabla\phi]_i
=\epsilon_{ijk}\partial_j\partial_k\phi=0,
$$
because the <Levi-Civita symbol> is antisymmetric in $j,k$ while equality of mixed <partial derivatives> makes $\partial_j\partial_k\phi$ symmetric. Hence
$$
\boxed{\nabla\times\nabla\phi=0}.
$$

 Back to article page