= Localized steady-current moment identities
{title2=$\int j_i=0,\quad\int x_i j_k=-\int x_k j_i$}
A localized steady <electric current density> satisfies $\nabla\cdot\mathbf j=0$. Integrate the divergences of $x_i\mathbf j$ and $x_ix_k\mathbf j$ over a region enclosing its support; all boundary fluxes vanish. The first identity removes the monopole term from the magnetic vector potential expansion. The antisymmetric first moment is equivalent to the <magnetic dipole moment> $\frac12\int\mathbf x\times\mathbf j\,dV$.
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