Two coaxial cylindrical conductors, of approximately same radius, are separated by a distance d in the radial dimension. The cylinders are placed into a liquid dielectric of susceptibility \chi and density \delta

The cylinders are held at a potential difference \Delta \phi. At what height h the liquid between the condutors will rise? (Disregard the surface tension).

where F_x is the upwards force and F_g is the weight of the liquid. These two must be equal:

where x is the height of the dielectric, R is the radius of the inner cylinder.

Is this rationale correct?