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Spherical Capacitor

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Original source (hyperphysics.phy-astr.gsu.edu)
Tags: physics science electricity-and-magnetism capacitance gauss-law hyperphysics.phy-astr.gsu.edu
Clipped on: 2016-10-28

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Spherical Capacitor

The capacitance for spherical or cylindrical conductors can be obtained by evaluating the voltage difference between the conductors for a given charge on each. By applying Gauss' law to an charged conducting sphere, the electric field outside it is found to be

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The voltage between the spheres can be found by integrating the electric field along a radial line:

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From the definition of capacitance, the capacitance is

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Does an isolated charged sphere have capacitance?
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Isolated Sphere Capacitor?

An isolated charged conducting sphere has capacitance. Applications for such a capacitor may not be immediately evident, but it does illustrate that a charged sphere has stored some energy as a result of being charged. Taking the concentric sphere capacitance expression:

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and taking the limits Image (Asset 7/8) alt= gives

Further confirmation of this comes from examining the potential of a charged conducting sphere:

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Capacitor Concepts
 
HyperPhysics***** Electricity and Magnetism R Nave
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