# Let's play with resistance

Two identical metal electrodes of spherical shape, and radius $$r$$ have been put in an infinite medium of cunductivity $$\sigma$$. They are placed on a distance much bigger than their radius are. Show that cunductivity can be expressed as $$G=\Lambda \sigma r$$ where $$\Lambda$$ is non dimensial constant that you should calculate.

Answer $$\Lambda$$ up to 2 decimals.

Hint: conductivity is given by formula $$G=\frac{I}{-\Delta \phi}$$, where $$I$$ is the net current, and $$-\Delta\phi$$ is negative potential difference beetwen them.

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