Ohm's law and emf for non static electric fields

[almarpa]

Hello all.

I am currently studying electromagnetism with Griffiths' books, and I have already donde electrostatic and magnetostatics. Now I am reviewing Ohm's law en emf concepts, but I have a doubt:

In griffths book, when explaining ohm's law and emf, it seems to me that he assumes steady currents and electrostatic fields. So, ohm's law is defined as J(r)=σE(r), and emf is defined as the closed line integral of the non electrostatic force acting on the circuit.

But, what happens in non stationary conditions (time dependent elctric fields and currents)?

Does Ohms law still remain the same?
I mean, would this equation J(r,t)=σE(r,t) be correct?

, and regarding emf, if electric field is not stationary anymore, would emf be defined in the same way?

Regards.

 

[Okefenokee]

Ohm's law still has to be the same. If it wasn't then a measured resistance could be time dependent.

Ohm's law is the same but in non stationary conditions the electric field has new dependencies on what the magnetic field is doing. You could define σE(r,t)=σE(J(r,t),B(r,t)) and then rewrite Ohm's law as J(r,t)=σE(J(r,t),B(r,t)). The right half there would require a solution for the electric field based on Faraday's law of induction and Ampere's law. It's still Ohm's law but now it's a real nasty differential equation.

 

[almarpa]

OK, I see.

Thank you so much.

And, what about emf?

Regards.