Layman explanation of some simple EM equations

[tim9000]

So its been a while since I studied maxwells equations, anyway:

So From my ignorant perspective, trying to derive conceptual meaning from these, I can see that the time dependant study there is some conductivity x the partial differential of the magnetic vector potential plus the cross product of mu*B which is H minus SOMETHING? equals the electron current density.

I don't really remember what the magnetic vector potential is (well, that is to say, I remember not really understanding it when I tried learning about it in the first place), or the last term...or what the cross product of H is.
I'm at a similar loss regarding the Frequeny Domain study.

To be honest all I really remember about the cross product is that it is perpendicular to the two vectors being multiplied.If anyone can offer a more indepth explanation of these formulas in English, I mean some maths is fine, but for a layman, that'd be great.

Cheers!

 

[MexChemE]

These might help

 

[tim9000]

These might help

Thanks for the reply, the second vid was a good refresher about curl (and to a lesser extent divergence), The first one didn't tell me anything I didn't already remember, but it made me try and wonder how Faraday's law might fit into those equations? (given that it has a current and cross product of B in it too).
But I'm still none the wiser about what the 'v' is in that equation (velocity?) or what the curl of H, cross product of Bxv and partial derivetive of A have to do with current density??

Cheers!

 

[tim9000]

So am I to assume that these equations aren't a modification/application of one specific Maxwell equation??

 

[jtbell]

What is the context of those equations? Where did you see them?

They seem to have something to do with electric and magnetic fields and electric currents in conductors. σ is the usual symbol for electrical conductivity, which is the reciprocal of resistivity: σ = 1/ρ.

 

[tim9000]

What is the context of those equations? Where did you see them?

They seem to have something to do with electric and magnetic fields and electric currents in conductors. σ is the usual symbol for electrical conductivity, which is the reciprocal of resistivity: σ = 1/ρ.

Yeah, they're from Comsol Multiphysics, depending on if you're simulating something that varies over time etc.