If I stuck two earth rods in a uniform field (e.g. a big flat area with grass or whatever) at ever increasing distances (e.g. 10m, 20m, 30m ..., 1000m etc) how would the result vary as a function of distance? An obvious answer would be linear (i.e. of the form R = AL + B where B is the resistance of the rods themselves). But a field isn't a wire, it's a plane - and that's a bit beyond my intuition, and beyond any easy maths.
It may help to visualise that (on regions of the earth small and uniform enough to be thought of as flat anyway )the cross-section of the resistor is approximately the shape of a rugby ball sliced longways, with the electrodes at the 'points' .
Then imagine slicing it into thick semi circles and looking at the resistance of a stack of half disks.
Increasing the length of the mid-section, also increases the diameter and so the area of that slice, which lowers the resistance faster then increasing the length raises it. Assuming the expanding region of influence it is not truncated by rock formations or caves, then as such the actual resistance is as others have said, almost independent of the bit in the middle, and dominated by what is happening where the current is converging or diverging very steeply, near the electrodes.
If you are brave (or well insulated, or use a lower voltage) you can see this, by livening up an electrode, and looking at the contours of surface voltage as you move away from it, nearly all the voltage drop is in the first couple of rod lengths - hence the assumption that rods 2 rod lengths apart can be considered as independent connections to the plate at the end of the universe, and even if they are only 1 rod length apart they are becoming fairly independent..
It may help to visualise that (on regions of the earth small and uniform enough to be thought of as flat anyway )the cross-section of the resistor is approximately the shape of a rugby ball sliced longways, with the electrodes at the 'points' .
Then imagine slicing it into thick semi circles and looking at the resistance of a stack of half disks.
Increasing the length of the mid-section, also increases the diameter and so the area of that slice, which lowers the resistance faster then increasing the length raises it. Assuming the expanding region of influence it is not truncated by rock formations or caves, then as such the actual resistance is as others have said, almost independent of the bit in the middle, and dominated by what is happening where the current is converging or diverging very steeply, near the electrodes.
If you are brave (or well insulated, or use a lower voltage) you can see this, by livening up an electrode, and looking at the contours of surface voltage as you move away from it, nearly all the voltage drop is in the first couple of rod lengths - hence the assumption that rods 2 rod lengths apart can be considered as independent connections to the plate at the end of the universe, and even if they are only 1 rod length apart they are becoming fairly independent..
