Electric field in a conductive solution

[phd_to_be]

Hi all
I am reading an article and I need some help to understand it.

They describe a device they made in which there are 2 platinum flat electrodes connected to a constant voltage supply. The electrode are placed parallel to each other in a conductive solution (water with some salts).
They say there is a constant electric field between the electrodes.

How can it be? if there is a current (and there is a current, they reported it) why should there be an EF?

 

[uart]

How can it be? if there is a current (and there is a current, they reported it) why should there be an EF?

You have that the wrong way around actually. Without an electric field there can be NO current in a conductive medium.

The current density is in fact proportional to the electric field,

$$J = \sigma \, E$$

Where $\sigma$ is the medium's conductivity.

 

[phd_to_be]

The current density is in fact proportional to the electric field,

$$J = \sigma \, E$$
Where $\sigma$ is the medium's conductivity.

So can I calculate the electric field by E=V/d, making it constant if the voltage doesn't change?
Can I ignore the current flowing between the plates?
Does this current change over time?


many question today :shy:

 

[uart]

So can I calculate the electric field by E=V/d, making it constant if the voltage doesn't change?

Yes you can approximate it as E=V/d if the plate separation is small compared to the plates linear dimensions.

Can I ignore the current flowing between the plates?

That depends on what you're doing. Why do you want to ignore it?

Does this current change over time?

Only if the voltage or the conductivity of the medium or positioning of the electrodes changes.

 

[phd_to_be]

Yes you can approximate it as E=V/d if the plate separation is small compared to the plates linear dimensions.

the plates are 17*5 mm = 85mm²
the distance between the plates is 50mm

can I approximate it as E=V/d?

 

[uart]

the plates are 17*5 mm = 85mm²
the distance between the plates is 50mm

can I approximate it as E=V/d?

Not really. The E field will be far from constant in the sense that it will vary quite a lot at different points within the conductive solution. That is, not time varying, but definitely having significant spatial variations.

 

[phd_to_be]

what do you think is a good enougth relation?

 

[DragonPetter]

what do you think is a good enougth relation?

The equation for a field between 2 plates is an approximation based on the geometry. It can be found by approximating the plates as charged disks to find the electric field of each, and then applying symmetry with Gauss' law to get the field between them. Think if the plates are infinite, then any point on the plate is the same as another, but if they are finite then going on the edge or the plate will have different charge than going in the center of the plate, and this will all change at different distances between the plates.

The electric field of a charged disks with radius R at a distance z from the plate is derived to be:

$$E = \frac{\sigma}{2\epsilon_{0}}(1-\frac{z}{\sqrt{z^2+R^2}})$$
so when z is finite and R approaches infinity, you get a constant electric field independent of distance. Applying Gauss' planar symmetry to find the electric field between the two plates makes the 2 cancel out.

Then the voltage potential is simply the integral of this E field over a distance. If you use finite values of R and z, you will have a different solution to the integral, and that is your clue to finding a good enough relation. I won't do the work, and you might need to modify the stuff I said, but I think that will put you in the right direction.

The stuff is pretty basic, and if you need to read about this explanation, I get this information from "fundamentals of physics" by halliday,resnick,walker.

 

[phd_to_be]

thanks.
I will read more :-)