An interesting problem on the subject of dielectrics concerns the force exerted by a parallel plate capacitor maintained at constant voltage on a dielectric slab inserted between its plates. Energy methods are used1
to calculate the attractive force, which depends on the square of the electric field, the plate area, and the relative permittivity εr.
A version of this problem is the calculation of the attractive force that pulls a liquid dielectric into vertical parallel plates dipped into the dielectric liquid. In some textbooks2
this is posed as an end-of-chapter problem, but in fact it may serve as the basis for a determination of the dielectric constant of a liquid, as described in Ref. 3, which also contains a derivation of the dependence of the height h
to which the liquid rises on the voltage V
(see Appendix): h = V2,
where ρ is the density and d
the plate separation. Here we shall describe a less sophisticated version of this method, using a homemade apparatus that can be used to demonstrate the effect. With some care it can be turned into a laboratory exercise in which students build the apparatus themselves (apart from the high-voltage supply) and measure the height as a function of the voltage.