# Resistance between 2 points in infinite 3-D gas volume

1. Mar 29, 2016

### Roger44

Hi

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. Apr 4, 2016