# Contact potentials

## Introduction

“In a paper of May 21, 1897 (Royal Institution of Great Britian) Lord Kelvin described a demonstration experiment that invites some thoughts, based on hindsight, about the connection between constant potentials and the voltage of galvanic cells.”

R.M. Lichtenstien in Nineteenth-Century Attitudes: Men of Science, Ross, S. 1991.

## The dry contact

A capacitor is built with two parallel plates of dissimilar metals, say copper and zinc. The zinc plate is ground. The copper plate is insulated. The copper plate is permanently connected to the ‘high’-terminal of an electrometer, here depicted by the electroscope symbol. $\Gamma _{Zn,Cu}=Ea$
Ross, 1991
When the plates are moved from contact (at a1) to a2, the electrometer reads a potential: $E\left( a_{2}-a_{1} \right)=\Gamma _{Zn,Cu}\frac{a_{2}-a_{1}}{a_{1}}\,\!$
The experiment can be altered slightly to use Kelvin’s null method for practical reasons.
Ross, 1991
The electric field at contact is now: $E-\frac{V}{a_{1}}=\frac{\Gamma _{Zn,Cu}-V}{a_{1}}\,\!$
When the copper plate is raised to a2, the electrometer will show the reading $\left( E-\frac{V}{a_{1}} \right)\left( a_{2}-a_{1} \right)=\left( \Gamma _{Zn,Cu}-V \right)\left( \frac{a_{2}-a_{1}}{a_{1}} \right)\,\!$
Repeated measurements determines the null potential and: $\Gamma _{Zn,Cu}=V_{null}\,\!$

Now the remarkable experiment!!!

The dry metallic contact of is replaced by a wet contact:
Ross, 1991

Before the copper plate is raised the electrometer no longer indicates the metallic zero but a new value, which Kelvin called the electrolytic zero.

Kelvin raised the copper plate, so that the water drop would break, and continued to raise it. The remarkable effect was that the electrometer started and remained at its electrolytic zero! This means there are no field lines across the gap! And ….

$\Gamma _{Zn,Cu}=\text{ voltage of the cell }Cu/water-drop/Zn \,\!$

Dry contact: Has electric field, voltage drop is zero, hence no power when current flows. Wet contact: No electric field, voltage is constant with separation, hence power when current flows. Current flows when circuit is completed; pile has a substantial voltage drop.