Experimental verification of the value of permittivity of free space How can one experimentally measure the value of permittivity of free space?
 A: We can calculate permittivity of free space using parallel plate capacitors.As we know C=(epsilon*Area)/width. We know the value of the capacitance C as it will be written on the capacitor. Area will be measured. Width will be measured.Then we can try finding permittivity of free space. this value won't come accurate. But we can try this at home also. try operating your fans condenser.
A: C = εo•εr•A/d. Conversely, ε0 = C•d/εr•A.
It will be a tough time - you need to find a capacitor with given value, the relative permittivity of the dielectric, the area of your plates and the distance between both of the plates. Breaking down the capacitor would only be worse; you're very likely to change its capacitance value when you start ripping off the cover and peeling of the plates.
If I were you, I would just accept in faith that electric permittivity of free space is 8.85•10^-12 as is.
But here's a second option:
Make a cap yourself - get two metal plates, measure width of the plates and distance between, no need for a dielectric, get a capacitance meter and measure capacitance. Then you can apply all that to above formula. Sadly, it will innacurate, extra water vapor in the air will still act as a dielectric. 
If I were still you, I would just accept in faith that electric permittivity of free space is still 8.85•10^-12 as is.
