# Capacitance of a sphere the size of earth

The capacitance of a sphere as big as the Earth is just a small fraction of a Farad (0.06 or something).

Yet there are available on the market capacitors of 1 Farad or greater. What am I missing here?

Well, for a start, using a dielectric medium can increase capacitance by several thousand times. Relative permittivity - Wikipedia

Next, they might use materials with extremely high surface areas.

nm

You are kinda talking about two different things. The capacitance of a sphere is its “self capacitance” which references itself against an imaginary infinite sphere. When you buy an off the shelf capacitor, the capacitance refers to the “mutual capacitance” where instead of comparing one conductor to an infinite sphere you are measuring one conductor inside the capacitor relative to the other conductor inside of it.

A very simple capacitor is just two plates close together. The capacitance is proportional to the area of the plates divided by the distance, so the closer you can get the plates the higher the capacitance. A 1 farad plate capacitor is going to be very large, though. The way they increase the capacitance is they roll the plates up into a tube to compact them, and then they add a dielectric material to increase the permittivity. This is how you end up with a 1 farad capacitor that isn’t monstrously huge.

Although, the 1 farad capacitor I saw was pretty big and heavy It was labelled as a 1,000,000 uF, which I found to be entertaining.

But thank you for clearing up how the capacitance of a single sphere could be calculated. My original post which I edited to just a “nm” incorrectly explained that capacitance always involved two different surfaces. I wasn’t familiar with the idea of self-capacitance, and using a sphere of infinite radius as the “other” plate but that makes sense.