Spherical capacitor energy problem

AI Thread Summary
The energy associated with a conducting sphere of radius R and charge Q in a vacuum is expressed as U = k*Q^2 / (2R). The discussion emphasizes calculating the work required to assemble the charge from an infinite distance to the sphere's surface. This involves considering the process of contracting an infinitely large sphere of charge Q to a smaller sphere of radius R, which is crucial for understanding the energy dynamics in electrostatics.
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Show that the energy associated with a conducting sphere of radius R and charge Q surrounded by a vacuum is

U = k*Q^2 / (2R)

:smile: thanks
 
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Where are you having difficulty with the problem?
 
Consider how much work you would have to do to bring all of the charge together from an infinite separation. In other words, how much work does it take to contract an infinitely large sphere of charge Q down to a small sphere of radius R?
 
It may be shown from the equations of electromagnetism, by James Clerk Maxwell in the 1860’s, that the speed of light in the vacuum of free space is related to electric permittivity (ϵ) and magnetic permeability (μ) by the equation: c=1/√( μ ϵ ) . This value is a constant for the vacuum of free space and is independent of the motion of the observer. It was this fact, in part, that led Albert Einstein to Special Relativity.
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