Why Does Expanding a Charged Spherical Shell Require Work?

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Homework Help Overview

The problem involves a charged spherical shell being expanded from a radius R to a radius H, with the goal of determining the work done by electric forces during this expansion. The context is rooted in electrostatics and energy considerations related to capacitors.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between potential energy and work done, with one attempting to calculate work based on changes in potential energy. Others question the validity of this approach, suggesting that the changing electric field during expansion necessitates integration to accurately determine total work done.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the need to consider energy stored in a spherical capacitor and the implications of changing electric fields on work calculations.

Contextual Notes

There are references to specific formulas for energy stored in capacitors and the capacity of spherical conductors, indicating that participants are working within the framework of established electrostatic principles. The discussion also highlights the complexity introduced by the changing conditions during the shell's expansion.

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Homework Statement


A spherical shell of radius R with uniform charge Q is expanded to a radius H.find the work done by electric forces during the shell expansion
given answer is 1/(8pi epsilon) *Q^2(1/R-1/H)
my attempt
work=-change in P E
=Q(V1-V2)
=1/(4pi epsilon) *Q^2(1/R-1/H)
please explain the additional 1/2 factor
 
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Here you have to consider the energy stored in a spherical capacitor.
What is the capacity of a spherical conductor?
What is the energy stored in a capacitor?
 
what is the mistake in my approach?
why not take change in potential energy as work done?
 
harini_5 said:
what is the mistake in my approach?
why not take change in potential energy as work done?
Because the electric field in continuously changing during the expansion of the spherical conductor. To find the total work done you have to take the integration.
Energy stored in the capacitor= 1/2*Q^2/C
Capacity of the spherical conductor = 4πεοR
 

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