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Resistance between 2 points in infinite 3-D gas volume

  1. Mar 29, 2016 #1

    Back in 2011 here https://www.physicsforums.com/threa...n-an-infinite-volume-of-resistive-gas.513388/ the question of the resistance between two points in an infinite volume of resistive gas was raised but petered out without a solution.

    The solution could be the conductance of a simple rod of gas linking the two electrodes multiplied by a Shape Factor of 4 pi r /(1 - (r/d)^2 - (r/d)^4 - 2r/d )

    where r is the radius of the two spherical electrodes and d their separation. For example, if the electrodes are of radius 1 cm and 10 cm apart, the current would be about 15 times what it would be if two electrodes were just linked by a rod of 2cm diam. My results need checking.

    This result comes from thermal conductivity, for example http://www.mhhe.com/engcs/mech/holman/graphics/samplech_3.pdf, where this case would be the equivalent of the thermal conduction between two spheres buried in an infinite 3-D medium. See at the bottom of page 79. I've no idea how they get to the above result.

    For conduction between two ROUND conductors on an infinite 2-D plane the Shape factor is a much simpler coshine function and at the end of this rather messy thread https://www.physicsforums.com/threa...-two-point-voltages-on-infinite-plane.832960/ you can find the maths that get to this result .
  2. jcsd
  3. Apr 4, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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