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I have $E$ (electric field intensity) in water.
I want to find $J$ (current density).
I don’t know if Ohm's law ($J=\sigma E$) is valid for water.
If it is not valid, how do I may find out $J$?

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  • $\begingroup$ You may use the hydraulic analogy. en.wikipedia.org/wiki/Hydraulic_analogy $\endgroup$ – Jitendra Jun 23 at 11:30
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    $\begingroup$ @Jitendra yes but this is not useful since the OP wants the current in actualmwater. $\endgroup$ – ZeroTheHero Jun 23 at 12:18
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    $\begingroup$ It is probably true in the bulk of the water, but the boundary conditions will depend on things like the electrolysis reactions between the water and some other material so it may not be very a useful relationship even if it is "true". $\endgroup$ – alephzero Jun 23 at 13:29
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The Ohm law is approximately(*) valid for water in the local form $J=\sigma \cdot E$ for the free liquid, but not in non local form $I=R \cdot U$, if electrodes and DC current are applied.

The latter is due involved electrochemistry, mainly but not limited to factors as:

  • Equilibrium potential of electrodes

  • Potential difference for electrolysis

  • Kinetics of electrode reactions

  • Transient electrode effects

  • Forming electrode layer potentials

  • Forming potential gradient due concentration gradient

That is why the liquid specific conductivity is measured differentially by AC voltage of frequency typically 1-3 kHz in the analytic technique called conductometry, using an electrode combo with the known geometry and known conversion factor conductance -> conductivity.

It may be integrated into automated titration techniques, following conductivity changes during progressive addition of a solution of known properties.


(*) The topic is rather complex solution chemistry. I say approximately,as there are some minor nonlinearities in driven motion of ions, based on nonlinear interaction of ions ( or rather of their hydrated forms) with water molecules and other ions.

Particularly for water ions, as they disappear and other ones appear in other place, as there is dynamic ion exchange with water molecules.

But in first approximation, it can be taken as linear.

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  • $\begingroup$ How do you say that Ohm's law is approximately valid for water in the local form? I mean where did you read about it ? And what do you mean by approximately ? I would be grateful of you could suggest some readings about this. $\endgroup$ – Saikiran Bojja Jun 24 at 5:49
  • $\begingroup$ The topic is rather complex solution chemistry. I say approximately,as there are some minor nonlinearities in driven motion of ions, based on nonlinear interaction of ions ( or rather of their hydrated forms) with water molecules and other ions. Particularly for water ions, they are cheating, as they disappear and other ones appear in other place, like in the table about the race of the turtle and the rabbit(?). But in first approximation, it can be taken as linear. $\endgroup$ – Poutnik Jun 24 at 6:35
  • $\begingroup$ That makes sense. I should look into chemistry to find out more details. $\endgroup$ – Saikiran Bojja Jun 24 at 8:13
  • $\begingroup$ Note that conductivity will change dramatically with dissolved CO2 from air, or due residual salts e.g. from reverse osmosis and final filtering. Another source of parasitic conductivity can be ions from container glass. $\endgroup$ – Poutnik Jun 24 at 12:19

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