The laws:
$\nabla \times \bar{E} = \bar{I}_{m} - \frac{\partial \bar{B}}{\partial \bar{t}}$
$\nabla \times \bar{H} = \bar{J}_{f} + \frac{\partial \bar{D}}{\partial \bar{t}}$
so how can I remember with fingers or any other deduction method which is minus and which is plus? Since there is now the nabla, I am a bit lost how the cross product hand-rule work.
The term $\bar{I}_{m} = 0$ if magnetic monopoles do not exist. It is there to show that the formulas are of the same structure, cannot just remember which is minus and which is plus.
[Update]
Is it easier to deduce the laws if I suppose that the circuit moves and not the field?
$\bar{v} \times \bar{E} = \bar{I}_{m} - \frac{\partial \bar{B}}{\partial \bar{t}}$
$\bar{v} \times \bar{H} = \bar{J}_{f} + \frac{\partial \bar{D}}{\partial \bar{t}}$
I am unsure whether the formulae are right so please check it. Could this way result in some easy deduction?