Non stationary currents and Ohm's law.

[almarpa]

Helo all.

Stationary currents are those whose current density is constant in time. On the other hand, ohm law claims that in certain materials, current density is proportional to electric field within the material.

So, if the electric field is stationary (constant in time), the current density must be constant in time, and the current stationary. But, in the case of a non stationary electric field, the current density should be time dependent, and the current producen should be non stationary. Is it right?

And a second question. Does the ohm law for currents and potential difference holds in the case of non stationary currents? If so, is the resistance fórmula for a piece of conducting material holds for non stationary currents?

Thanks all!

 

[sophiecentaur]

Hi
I am not familiar with your terminology here. I think you are just referring to Constant values of Current and Field?
Actually, ifaik, Ohm's law (which is only the description of an observed behaviour) doesn't actually 'claim' anything. It happens that metals follow Ohm's Law over a wide range of currents.

I think you are suggesting that there will be a delay between any change of applied field and the current. This would imply some electron Mass is involved and a finite change of velocity - if you are only speaking of a resistive conductor. The momentum of electrons is extremely small as they travel through metals at a few mm/s and they are very low mass but I guess you could easily calculate the delay with a simple mechanical model, using the force involved and the mass of an electron. A SUVAT calculation could be worth while trying, to get an idea of the sort of times involved. (Force = Field times charge, final velocity = (say) 1mm/s. The electrons have a range of initial velocities, of course but it may be worth your while to do the sum. The Drude Model was a sort of classical approach about a hundred years ago and that makes reasonable predictions. You could read that article, which seems relevant.

There is an inherent delay in the effect of a change in field, due to the speed limit of the eM wave, which is a bit less than c and there is also effect of Inductance in a circuit.

 

[almarpa]

Thanks for your help, but I meant a different thing.

Let me explain my doubt. Currently I am studying electromagnetism (with Griffiths and Purcell books). I have already studied Electrostatics (constant in time electric fields produced by stationary charges), and magnetostatics (constant in time magnetic fields produced by steady currents). Now I am studyig the unit about electric currents. In this unit continuity equation is introduced, as well as Ohm's law and electromotive force.

However, although they no not say it explicitly, I have the feel that in this unit all the books consider steady currents when talking about Ohm's law and emf. Is it so? Is Ohm's law an empirical result only valid for staedy currents, or is it also valid for, say, non steady currents driven through a metal?

if so, are all the equations derived from it (V=IR, R=L/σA) valid for non stationary currents?

Regards.