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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 \(\frac{Q}{4\pi\epsilon}\left (\frac{1}{a}-\frac{1}{b}\right )\), and so the capacitance is

    \[C=\frac{4\pi \epsilon}{\frac{1}{a}-\frac{1}{b}}.\label{5.4.1}\]

    If \(b \to \infty\) we obtain for the capacitance of an isolated sphere of radius a:

    \[C=4\pi \epsilon a.\label{5.4.2}\]

    Exercise: Calculate the capacitance of planet Earth, of radius 6.371 × 103 km, suspended in free space. I make it 709 \(\mu\text{F}\) - 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; a detailed edit history is available upon request.

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