Electrostatic Clamps Using Dielectrics

[jmtome2]

b]1. Homework Statement [/b]
Electrostatic clamps are used for holding workpieces while they are being machined, for holding silicon wafers during electron beam microfabrication, etc. They comprise an insulated conducting plate maintained at a potential of several thousand volts and covered with a thin insulating sheet. The workpiece or the wafer resets on the sheet and is grounded. It is advisabled to apply a film of oil to the sheet to prevent sparking.

One particular type operates at 300 volts and has holding power of 2 atmospheres. If the insulator is Mylar (Class-A; $$\epsilon_r=3.2$$, what is its thickness?

Homework Equations

$$F=-\frac{dW}{dx}$$

$$W=\frac{1}{2}CV^{2}$$

$$Q=CV$$

The Attempt at a Solution

Can I treat this system as a parallel plate conductor with a dielectric in the center? I don't see how to extract the thickness from this.

$$F==-\frac{dW}{dx}=\frac{1}{2}\frac{Q^2}{C^2}\frac{dC}{dx}=\frac{1}{2}V^2\frac{dC}{dx}$$

But the capacitance is constant $$C=\frac{Q}{\Delta V}$$ meaning F becomes zero... which does not makes sense...

Is there another way to calculate the capacitance?

 

[jmtome2]

I know the capacitance of a parallel plate configuration with dielectric filling the middle is $$C=\frac{A\epsilon_0\epsilon_r}{d}$$, but I also know that the grounded "plate" on top throws this off... I'm just not sure how