# Let's play with resistance

**Electricity and Magnetism**Level 5

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.