Calculating force exerted by potential difference (electric field).

[ParrotPete]

Homework Statement

A horizontal dielectric slab, with \epsilon_{r} = 5 and height 2 cm, contains an upper metalic surface. Below the slab a copper sheet is suspended, height 0.1 mm. Use $$\rho_{cu}$$ = 8.9g/cm^3 Calculate the potential difference between the top of the slab and the sheet necessary for the sheet to hang without support. Assume an infinitedecimal pillar of air between the slab and the sheet.

Homework Equations

Newton 1. $$\rho_{Cu}*V_{sheet}*10^{3}+F = 0$$.
$$W_{e} = \int_{dV} \vec{E} * \vec{D} dV$$
$$F = -\nabla W_{E}$$
$$U_{top}-U_{sheet} = - \int^{top}_{sheet} \vec{E} d\vec{l}$$
$$\int \vec{D} \vec{dS} = Q.$$

The Attempt at a Solution

Am I on the right track here? I calculate the different fields in the various surfaces. Then I just calculate the potential difference (line integral) and after that I calculate the total electrostatic energy contained in the various fields and after that I just take the gradient to calculate the force from this, and plug it into Newton 1.

 

[NateD]

It's a bit hard for me to figure out how to calculate the potential difference from the line integral. I am given \vec{E} and \vec{D}, but it seems that I need to also get \vec{B}. Is this correct?