Let us say we have a small electrolyte (NaoH) tank in which there are electrodes with a specific voltage. I would like to know what is the electrical field intensity under applied voltage.
Theoretically, you can find the answer by solving the Poisson-Boltzmann equation for the geometry of your tank.
The solution for specific geometry cases can be found in D. Andelman,
Introduction to electrostatics in soft and biological matter (book chapter),
Soft Condensed Matter Physics in Molecular And Cell Biology (2006).
In equilibrium, there is "no license to" build an electrical field E, inside the bulk of an ideal strong electrolyte (NaOH[1]), like inside the bulk of an ideal metal (Cs, Li, Au, Ag, etc.) material. So, in equilibrium, both[4], allow an E, to form , only, on their boundaries (surfaces, nano-meters, only[5], on the electrodes), or in devices.
1. NaOH (water solution) is a very strong base. In the water it will disassociate (completely[2]) into : Na+ and OH- ions.
2. It is a very[3] strong electrolyte (pH~14).
3. NaOH (lye) is used, very often, in cleaning products, like soap and oven cleaners.
4. We have fast equilibrium in metal (
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