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Physics LibreTexts

5.4: Concentric Spherical Capacitor

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Unlike the coaxial cylindrical capacitor, I don’t know of any very obvious practical application, nor quite how you would construct one and connect the two spheres to a battery, but let’s go ahead all the same. Figure V.4 will do just as well for this one.

The two spheres are of inner and outer radii a and b, with a potential difference V between them, with charges +Q and Q on the inner and outer spheres respectively. The potential difference between the two spheres is then Q4πϵ(1a1b), and so the capacitance is

C=4πϵ1a1b.

If b we obtain for the capacitance of an isolated sphere of radius a:

C=4πϵa.

Exercise: Calculate the capacitance of planet Earth, of radius 6.371 × 103 km, suspended in free space. I make it 709 μF - which may be a bit smaller than you were expecting.


This page titled 5.4: Concentric Spherical Capacitor is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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