Simple doubt in induced charge

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Discussion Overview

The discussion revolves around the behavior of induced charges on a conducting spherical shell when a positive point charge is brought close to it. Participants explore different scenarios based on the presence of an additional charge within the shell, considering both theoretical implications and the effects of charge magnitudes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes two possible outcomes when a positive charge q approaches a neutral conducting spherical shell containing a charge +Q, suggesting that either fewer positive charges will be present on the side near q or negative charges will be induced on that side.
  • Another participant notes that the outcome depends on the relative magnitudes of q and Q, indicating that a small q leads to the first scenario while a large q leads to the second.
  • A different participant introduces the concept of Coulomb force acting between the charges, suggesting that work must be done to bring them together due to repulsion.
  • One participant confirms the previous points and emphasizes that the charges rearrange to cancel the external electric field within the conducting material.
  • Another participant mentions the method of image charges as a way to analytically solve the problem, explaining how the additional charge can be distributed without affecting the balance of forces on the conduction electrons.

Areas of Agreement / Disagreement

Participants generally agree on the principle that the induced charges rearrange to maintain a field-free interior in the conductor. However, there is no consensus on which of the two proposed scenarios regarding the induced charges is correct, as it depends on the relative magnitudes of the charges involved.

Contextual Notes

The discussion includes assumptions about the magnitudes of the charges and the nature of the induced charges, which are not fully resolved. The implications of the Coulomb force and the method of image charges are also mentioned but not elaborated upon in detail.

Vibhor
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When a positive point charge q is brought close to a neutral conducting spherical shell then negative charges will be induced on the part of the shell closer to q and equal positive charges will appear on side of the shell farther from q.I understand this part.

But if the conducting spherical shell contains a charge +Q,then,if charge q is brought close to the shell ,what will happen ?

There are two possibilities

1) Fewer positive charges will be present on the side of shell near the charge q ,say Q1 ,and higher concentration of charges,say Q2, on the side of shell farther from q ,such that Q1+Q2=Q

2) Negative charges will be induced ,say -Q1,on side of the shell close to q and positive charge,Q1+Q will be present on the side farther from q.

I am not sure which of the possibilities is correct.

Please give your suggestions.
 
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It depends on the magnitude of q relative to Q. If q is very small, you get your situation #1. If q is very large, you get your situation #2.
 
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You have brought a charge +q near a charged conductor having charge +Q right? When then get closer to each other there will one force acting known as coulumb force. So the chagres might repel each other.
So when you bring them togather you have to do work.
Other things go on as jtbell suggested.
 
Thanks jtbell :-)

jtbell said:
It depends on the magnitude of q relative to Q. If q is very small, you get your situation #1. If q is very large, you get your situation #2.

And in both the cases the charges rearrange themselves such that the external electric field is canceled within the conducting metal .Correct?
 
Yes, the interior is field free, if there are no charges inside. The problem can be solved analytically by the use of the method of image charges. Start with the problem with zero charge on the shell. The problem with a total charge Q on the shell is then solved by simply distributing this additional charge homogeneously over the shell. This is clear from the physics of this phenomenon: If you put the charge close to the shell the conduction electrons will rearrange such that the total force on them vanishes. Now you can homogeneously distribute any amount of additional charges on the surface without changing this balance.

A complete treatment can be found in Jackson, Classical Electrodynamics
 

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