Moving a point charge out of a cavity in a conductor

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SUMMARY

The discussion focuses on calculating the work required to move a point charge q from the center of an uncharged spherical conducting shell to infinity. The relevant equations include W = qV and V = ∫E·dl, where E is the electric field. The participants emphasize the need to consider both the internal and external voltages of the shell, noting that the voltage inside a conductor remains constant. The method of image charges is suggested as a potential approach to determine the electric field at the charge's location.

PREREQUISITES
  • Understanding of electrostatics, specifically the behavior of conductors in electrostatic equilibrium.
  • Familiarity with the concept of electric potential and its relationship to work done in moving charges.
  • Knowledge of integration techniques, particularly in the context of electric fields and potentials.
  • Awareness of the method of image charges for solving electrostatic problems.
NEXT STEPS
  • Study the method of image charges to understand how it simplifies electrostatic problems involving conductors.
  • Learn how to calculate electric fields and potentials using Gauss's law in spherical coordinates.
  • Explore the concept of electric potential energy and its implications in electrostatics.
  • Investigate the properties of conductors in electrostatic equilibrium, focusing on voltage distribution.
USEFUL FOR

Students studying electrostatics, physics educators, and anyone involved in solving problems related to electric fields and potentials in conductive materials.

Momentous
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Homework Statement



A point charge q is at the center of an uncharged spherical conducting shell, of inner
radius a and outer radius b. How much work would it take to move the charge out to
in nity? (fi nd the minimum work needed. Assume charge can take out through a tiny hole
drilled in the shell. Think about the work you need to assemble the system)

Homework Equations



W = qV
V = ∫E. dl
dl = (r^ dr + θ^ dθ + ϕ^ d ϕ)


The Attempt at a Solution



The overall equation is W = qV. I'm just a little unsure about getting V (q is given).

My guess is that there has to be two integrations for the Voltage inside and outside of the shell. I'm not really too sure about all of that, because isn't the Voltage in a conductor always constant.

So is it possible V = (V(out) + V(in)) = (V(out) + C) where C is just some arbitrary constant. Or can you actually find the constant value of that voltage with the information given?
 
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Momentous said:

Homework Statement



A point charge q is at the center of an uncharged spherical conducting shell, of inner
radius a and outer radius b. How much work would it take to move the charge out to
in nity? (fi nd the minimum work needed. Assume charge can take out through a tiny hole
drilled in the shell. Think about the work you need to assemble the system)

Homework Equations



W = qV
V = ∫E. dl
dl = (r^ dr + θ^ dθ + ϕ^ d ϕ)


The Attempt at a Solution



The overall equation is W = qV. I'm just a little unsure about getting V (q is given).

My guess is that there has to be two integrations for the Voltage inside and outside of the shell. I'm not really too sure about all of that, because isn't the Voltage in a conductor always constant.

So is it possible V = (V(out) + V(in)) = (V(out) + C) where C is just some arbitrary constant. Or can you actually find the constant value of that voltage with the information given?

I would think about using your E.dl form instead. To find E at the point where the charge is use the method of image charges. Have you covered that topic?
 
I can't say that I know what that method is. Isn't my method using the E.dl form?
 

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