= Solution
Apply the <symmetric gradient and curl decomposition> separately to the <electric field> and the <magnetic field>:
$$
\boxed{S^E_{ij}=\frac12(\partial_iE_j+\partial_jE_i),\qquad
S^B_{ij}=\frac12(\partial_iB_j+\partial_jB_i)}.
$$
The corresponding axial parts are
$$
\boxed{\mathbf u^E=\frac12\nabla\times\mathbf E=-\frac12\partial_t\mathbf B,
\qquad
\mathbf u^B=\frac12\nabla\times\mathbf B=\frac1{2c^2}\partial_t\mathbf E}.
$$
The second equalities use the vacuum <Maxwell equations>. Their <divergence> constraints also show that both symmetric <gradient> <tensors> are traceless.
Back to article page
