# Capacitance of a sphere the size of earth

**URL:** <https://boards.straightdope.com/t/capacitance-of-a-sphere-the-size-of-earth/645369>\
**Category:** Factual Questions\
**Created:** [December 28, 2012, 10:51am UTC](https://boards.straightdope.com/t/capacitance-of-a-sphere-the-size-of-earth/645369 "2012-12-28T10:51:22Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Dog80](https://avatars.discourse-cdn.com/v4/letter/d/6bbea6/32.png) [@Dog80](https://boards.straightdope.com/u/Dog80)\
**Post date:** [December 28, 2012, 10:51am UTC](https://boards.straightdope.com/t/capacitance-of-a-sphere-the-size-of-earth/645369/1 "2012-12-28T10:51:22Z")

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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? 😕

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**Author:** ![AaronX](https://avatars.discourse-cdn.com/v4/letter/a/7bcc69/32.png) [@AaronX](https://boards.straightdope.com/u/AaronX)\
**Post date:** [December 28, 2012, 11:12am UTC](https://boards.straightdope.com/t/capacitance-of-a-sphere-the-size-of-earth/645369/2 "2012-12-28T11:12:50Z")

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Well, for a start, using a dielectric medium can increase capacitance by several thousand times. [Relative permittivity - Wikipedia](http://en.wikipedia.org/wiki/Relative_permittivity)

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

> **[Supercapacitor](https://en.wikipedia.org/wiki/Supercapacitor)**
>
> A supercapacitor (SC), also called an ultracapacitor, is a high-capacity capacitor, with a capacitance value much higher than other capacitors but with lower voltage limits. It bridges the gap between electrolytic capacitors and rechargeable batteries. It typically stores 10 to 100 times more energy per unit volume or mass than electrolytic capacitors, can accept and deliver charge much faster than batteries, and tolerates many more charge and discharge cycles than rechargeable batteries.
> Supe...

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**Author:** ![drewtwo99](https://avatars.discourse-cdn.com/v4/letter/d/d07c76/32.png) [@drewtwo99](https://boards.straightdope.com/u/drewtwo99)\
**Post date:** [December 28, 2012, 11:15am UTC](https://boards.straightdope.com/t/capacitance-of-a-sphere-the-size-of-earth/645369/3 "2012-12-28T11:15:05Z")

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nm

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**Author:** ![engineer\_comp\_geek](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/engineer_comp_geek/32/504_2.png) [@engineer\_comp\_geek](https://boards.straightdope.com/u/engineer_comp_geek)\
**Post date:** [December 28, 2012, 11:17am UTC](https://boards.straightdope.com/t/capacitance-of-a-sphere-the-size-of-earth/645369/4 "2012-12-28T11:17:30Z")

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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.

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**Author:** ![drewtwo99](https://avatars.discourse-cdn.com/v4/letter/d/d07c76/32.png) [@drewtwo99](https://boards.straightdope.com/u/drewtwo99)\
**Post date:** [December 28, 2012, 11:26am UTC](https://boards.straightdope.com/t/capacitance-of-a-sphere-the-size-of-earth/645369/5 "2012-12-28T11:26:31Z")

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> [@engineer\_comp\_geek](#):
>
> 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.