# Measuring the vacuum permittivity

So I was reading the EF experiment that's used at the MIT to measure the vacuum permittivity and I was thinking about trying it just to see how it works:

http://ocw.mit.edu/courses/physics/8-02x-physics-ii-electricity-magnetism-with-an-experimental-focus-spring-2005/labs/experiment_ef.pdf

I have some questions about it and I hope you can help me with them:

1. It says "To find the electric force on the foil, assume that the charge density, σ , on the foil, is the same as that of the lower washer". How good that assumption is?

2. It says "Charges on the foil feel only horizontal forces from other charges on the bottom plate, so the vertical force on the foil is due to the electric field of just the top charge sheet". What horizontal forces are they talking about? I thought both the bottom plate and the upper plate were all exerting a vertical force on the foil and that's why I don't understand why the force is due just to the electric field of the upper plate $(V/2d)$ and not from the one of the two plates $(V/d)$.

3. Finally, why washers? I think it really doesn't matter if they're just two discs, does it?

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## 1 Answer

1. The experiment calls for noting when the foil just lifts off the bottom plate. Since the foil and the washer are both presumably good conductors, the charge density should be the same until they stop touching. So the "goodness" of this assumption depends on the variation in the voltage across the capacitor after the foil lifts off.

2. The foil should feel forces from both plates, so I think your source is wrong in this. Horizontal forces come from the fact the plates are not infinite, and therefore some of the field goes beyond the plates.

3. Washers are both readily available and fairly good conductors, so they're used in a lot of "do it at home" type experiments.

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