Charge inside a spherical conducting shell

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Discussion Overview

The discussion revolves around the behavior of electric fields in relation to a charge placed inside a spherical conducting shell. Participants explore concepts related to electric fields, potential energy, and the implications of moving charges within and outside the conducting material.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant posits that placing a positive charge inside a spherical conducting shell results in zero electric field inside the shell due to induced negative charge on the inner surface.
  • Another participant clarifies that while the electric field in the conducting material is zero, the electric field in the empty space inside the shell is not necessarily zero.
  • A question is raised about the work done when moving a charge from the inner radius to the outer radius of the shell, suggesting that it may be zero.
  • One participant suggests using energy considerations to determine work done, indicating that potential energy changes must be considered.
  • It is noted that moving the charge through a hole in the shell would not result in zero work, as the hole is not filled with conducting material, thus the electric field may not be zero in that region.
  • Another participant agrees that if the charge is moved through the metal itself, the work done would be zero.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of electric fields in various regions of the conducting shell and the implications for work done when moving charges. The discussion remains unresolved regarding the specifics of work done in different scenarios.

Contextual Notes

Participants do not fully resolve the implications of moving charges through different regions of the shell, and there are assumptions about the nature of the electric field in the space of the hole versus the conducting material.

zeeva
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If a charge is placed inside a spherical conducting shell, is the total electric field inside it zero? I am thinking that if the charge is positive, then the conducting shell will have an equal amount of negative charge on its inner surface, therefore the E field should be zero inside, right?
 
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You mean the electric field in the space filled by the conducting material? In that case you're right, it would be zero. That's pretty general, actually: any space filled with conducting material will have zero electric field, because if the electric field were nonzero, it would push around electrons inside the conductor until they canceled out the external field.

Of course the E field in the empty space inside the shell would not be zero.
 
Does that mean that if the shell had a hole through it and we wanted to move the charge from the inner radius to the outer radius, the work would be zero?
 
It would be better to use energy considerations here. The value of potential energy would be different in the initial and the final configurations.

Work done=Change in Potential Energy
 
zeeva said:
Does that mean that if the shell had a hole through it and we wanted to move the charge from the inner radius to the outer radius, the work would be zero?
Not if you move the charge through the hole. The space of the hole is not filled with conducting material, so there's no reason the electric field inside it would be zero.

Of course, if you move the charge through the metal itself, and not through the hole, then the work done would be zero.
 

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