Constructing a 1nF Capacitor with >10kV Breakdown Potential

[Bryon]

Homework Statement

You are asked to construct a capacitor having a capacitance of around 1 nF and a breakdown potential in excess of 10,000V. You're thinking of using the sides of a tall Pyrex laboratory cylindrical beaker. You can line the inside and outside of the sides of the beaker with aluminum foil to act as plates. The Pyrex of the beaker sides will keep the foil in place and with the added advantage of acting as a dielectric.
The height of your beaker is 17 cm. Its inside radius is 3.6 cm and its outer radius is 3.89 cm.

Homework Equations

Q = CV = ε₀κA/d
A = 2πrh

The Attempt at a Solution

A_inner = 2*π*(0.036)*(0.17) = 0.03845309
A_outer = 2*π*(0.0389)*(0.17) = 0.04150744

C = ((5.6)*(8.85x10^-12)*(A_inner + A_outer))/(0.0389-0.036)
C = 1.367237x10^-9F

Was I correct in using only the difference between the inner and outer radius? I also thought that adding the total area of the inner and outer radius was the correct approach since the capacitance depends on the area as well. What did I do wrong?

 

[gneill]

The area in a parallel plate capacitor refers to the overlapping area of the plates, not the total of the two plate areas.

Cylindrical capacitors are a bit different because, a) the plates have different areas yet they completely overlap, so that b) the electric field will not be uniform from one plate to the other.

Presumably if the cylinder diameter is much greater than the thickness of the wall, then the plate sizes will be approximately equal and the field will be approximately uniform and you can use the average area of the plates to find the capacitance.

For more accuracy, you might want to check out the http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capcyl.html" .

http://www.ajdesigner.com/phpcapacitor/cylindrical_capacitor_equation_l.php"

 

[Bryon]

Great! Thanks that is what I needed. Plus it shows where it comes from.