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I am making bipolar voltage measurements in which the distance between my probes small enough that I think the geometry of the probe contact tips is non-trivial. As illustrated below, my voltage probes are cylindrical and situated on either side of a dipole. I want to know the effective distance between the probes and have heretofore been computing this on-center (Distance A).

enter image description here I know that a complete-electrode-model of effective distance would have to account for contact impedance and non-infinite within-probe shunting, but this is beyond the scope of what I am trying to accomplish.

I believe that if I assume that the electrodes are perfectly conductive and have zero impedance, the effective distance between them is the distance between their nearest points (Distance B).

Is this reasoning correct? Am I making other (unstated) assumptions?

In my particular experiment, distance A is 5mm, distance B is 2.6 mm, and the probe contacts are 2.4 mm long and have a diameter of 1.28 mm. The probes are bathed in a conductive fluid.

Thank you.

EDIT: I added equipotential lines to the figure (the voltage values are for illustrative purposes only). I know the conductivity of the media and have solved the quasi-electrostatic forward and have a good estimate of the quasi-electrostatic inverse. I am now trying to use voltage measurements to assess the strength of my dipole but am unsure of what inter-contact distance to use in my equations. Assume that the dipole is centered between the probes.

EDIT: My fluid medium conductivity is on the order of 10^-1 and my contact conductivity is on the order of 10^7.

Neuromancer
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  • Are you trying to determine the electric field in the area marked "dipole" or the total conductivity between the probes? The latter will be non-trivial. – Spehro Pefhany Feb 08 '17 at 01:07
  • @Spehro, The electric field. The conductivity of the medium is known, to a reasonable approximation. The intercontact distance is relevant because I am ultimately trying to determine the dipole strength. – Neuromancer Feb 08 '17 at 01:17

1 Answers1

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The conductivity of the probes is not going to be trivial, you'll need to know your field strength from the dipole and assume that it is indeed pointed in the direction that you have indicated. If the dipole is not pointed in that direction then it will make the calculations ugly because symmetry will be thrown out the window as a gradient will exist across the disk and cylinder.

Secondly dipoles aren't point charges, I'm not sure what the field equation is for yours, but it will need to be understood to a reasonable degree of accuracy. Maybe you've worked out the equations already, if you have great, if you haven't I'll include them.

Gauss's law will be your best friend here:From www.physics.umd.edu/courses/Phys260/agashe/S10/notes/lecture18.pdf

Integrate the fields from the dipole across the surface of the disk of the probe. Then the cylinder. I would imagine that after the cylinder is worked out it will be found that the cylinders surface will 'collect' a small percentage of your total charge and can be neglected.

This will work if you assume that the disk\probe has no charge (everything in the real world has a charge that will have to be minimized). It also neglects edge effects from the corner and these may or may not contribute substantial error.

The second thing you will want to add in is effects from materials, like electric permeability and whatever your solution does to the electric field

After the paper calculations are done, if you have some time left, I'd throw the whole thing into a 2d static electric field solver and then compare that to the hand calculations and see if the models are close if they are, then you can use the simpler assumptions.

Voltage Spike
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  • In the model version of my experiment, I have integrated the fields in the probe volume, with the (terrible) assumption that the probe conductivity is equal to the fluid medium's, but I don't think this value is useful. Because the probe's conductivity is about 8 orders of magnitude greater than the medium's, I figure that treating it as having infinite conductivity is reasonable and under that assumption the probes are equivalent to a point electrodes at distance A. Does this sound reasonable to you? Also, what solver would you recommend? – Neuromancer Feb 08 '17 at 19:57
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    Oh, I forgot, make sure you mitigate electrochemical effects, it could become a problem. Come up with an error budget. I think infinite conductivity is reasonable to start with, if your making measurements and things don't add up then you'll need to find out why. As far as the 2d field solver goes really depends on your budget, if you have access to comsol or ansys I'd use those. If you don't here is a (good list of electric field software)[http://electronics.stackexchange.com/questions/48523/open-source-or-free-electric-field-mapping-software]. If you like the answer upvote ;) – Voltage Spike Feb 09 '17 at 06:27