Moving-conductor Ohm law ($\mathbf{E}+\mathbf{u}\times \mathbf{B}=\mathbf{J}/\sigma$)

In the nonrelativistic scalar-conductivity approximation, neglecting Hall and other nonideal electromotive effects, $\mathbf{J}=\sigma (\mathbf{E}+\mathbf{u}\times \mathbf{B})$. The ideal finite-current limit gives $\mathbf{E}=-\mathbf{u}\times \mathbf{B}$ and hence the ideal magnetohydrodynamic induction equation.