# Electrostatic potential with floating metals:computation and measurement

1. Jul 25, 2012

### Barloud

Hi all,
I am considering the situation illustrated in the schematic below. A surface density of permanent charges σ is embedded into a dielectric (with relative permittivity εr) itself sandwiched between two electrically floating metallic plate. We have also L>>t1 and L>>t2.
My first goal is to determine an expression of the potential difference between the two floating metals. I start by considering that, without the metallic plates, the electrical field above and below the charge distribution is the same than for an infinite charged plane, as long as the field is measured very close from the charge density. Its amplitude is then |σ|/(2ε0εr ). For a fixed vertical position z, the electrostatic potential is in this case constant. This makes me thinking that the situation is not modified when the two floating metal plates are introduced in the problem, at least in between the two plates, as they are equipotential surfaces located along a line with constant z. In this case the absolute value of the potential difference between the two plates would simply be |(t1-t2)σ|/(2ε0εr).

Is this approach correct?

Then how can this potential difference be measured experimentally? Should it work by connecting the floating metals to an electrostatic voltmeter?