Jay Taylor's notes

back to listing index

Spherical Capacitor

[web search]
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

Image (Asset 1/8) alt=

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

Image (Asset 2/8) alt=

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

Image (Asset 3/8) alt=

From the definition of capacitance, the capacitance is

Image (Asset 4/8) alt=
Does an isolated charged sphere have capacitance?
 Index

Capacitor Concepts
 
HyperPhysics***** Electricity and Magnetism R Nave
 Go Back
Image (Asset 5/8) alt=

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:

Image (Asset 6/8) alt=

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

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

Image (Asset 8/8) alt=
 Index

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