Point Charge in Conducting Sphere: Experiencing Force?

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Discussion Overview

The discussion revolves around the behavior of a point charge placed within a cavity of a conducting sphere when the sphere is charged. Participants explore whether the point charge experiences a force and the implications of charge distribution on the sphere's surfaces.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions if a point charge in a cavity of a conducting sphere experiences a force when the sphere is charged.
  • Another participant asserts that the point charge will not experience a force due to the charge on the sphere but may experience a force due to induced charges on the cavity wall.
  • A participant explains that if the point charge is not centered, it will exert a non-radial force on opposite charges on the inner surface of the shell, leading to a net force on the point charge towards the wall of the shell.
  • There is a query about the presence of charge on the inner surface of the shell, given that the electric field inside the metal is zero.
  • A response clarifies that charge can exist on the inner surface due to redistribution of charge from the metal, ensuring the net electric force inside the metal remains zero.
  • Participants discuss that charge is present on both the inner and outer surfaces of the shell, but not within the solid metal part.

Areas of Agreement / Disagreement

Participants generally agree that the charge on the inner surface is influenced by the point charge, but there is some debate regarding the implications of charge distribution and the forces experienced by the point charge.

Contextual Notes

Participants discuss the relationship between charge density and electric field, noting that while the electric field inside the metal is zero, charge can still be present on the surfaces. The discussion does not resolve the complexities of charge interactions fully.

Who May Find This Useful

This discussion may be of interest to those studying electrostatics, particularly in the context of conductors and charge distribution in cavities.

ledin12
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If a point charge is placed in a cavity of a conducting sphere, and the sphere itself is given a charge , would the point charge in the cavity experience a force?
 
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No......
 
The charge inside will not experience a force due to that on the sphere. But it may due to the charge that it induces on the wall of the cavity
 
If the charge (let me denote it as Q) inside is not in the centre of the spherical shell, it will exert non-radial force on the charges B of opposite sign on the inner surface of the shell. The charges B will distribute on the surface in such way that they will shield perfectly the charge Q, so the electric field in the metal will be zero. This is possible only if the highest density of surface charge will be at the part of the surface which is closest to the charge Q. Hence the charge Q will exert net force on the metallic shell, and by the principle of action and reaction, the same but opposite force will act on the charge Q. This force will pull the charge towards the wall of the shell. If Q is movable, it will approach the wall and become part of it. Then it will be sucked away to outer surface and will spread uniformly over it.
 
Jano L.
But how can charge be present at the inner surface of the shell? i mean wouldn't net electric field be 0 and hence q=0 inside the metallic part? so how can B exist at the inner surface? could you explain why it happens.
Thanks.
 
The electric field inside the metal is indeed 0, implying that the charge density is zero there too.

In order to make this possible, some charge B of opposite sign has to come from the metal to its inner surface and redistribute itself there so that the net electric force due to A and B in the interior of the metal is zero.

From another point of view, the positive charge A attracts equal amount of negative charge B as close as possible, that is, to the inner surface.

Zero density inside of the metal does not exclude that charge is present at the surface of the metal. In fact the charge density [itex]\sigma[/itex] and the normal component of the electric field obey the relation

[tex] \sigma = 2\epsilon_0 E_n.[/tex]
 
so that means charge is present on the inner and outer surface but not in the solid metal part.
Right?
 
Exactly. The charge on the inner surface is -Q, the charge on the outer is +Q. In the metal the charge density is zero.
 
I get it now. Thanks a lot!
 
  • #10
Glad to be of help,
Jano
 

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