Saturday, 3 February 2018

electrostatics - Resistance between two points in an infinite metal sphere/cube


Let's imagine that we have a tridimensional metal object of infinite size, and decide to calculate the resistance between two arbitrary points. How would we go about doing this?


I have thought of two possibilities for calculating this, the first one being an adaptation of the conductivity (S/m) using the Pythagorean theorem to find a distance and isolating the resistance from there, treating it like we would treat an electrolytic liquid.


The second possibility I have been thinking about would be a 3-dimentional adaptation of the infinite-resistors problem (which I have only seen in 2d).


Would one of these methods result in giving a decent approximation, or would another method give better results?




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