Point Charge in Conducting Sphere: Experiencing Force?

In summary: L.In summary, when a point charge is placed in a cavity of a conducting sphere, it will not experience a force due to the charge on the sphere itself. However, it may experience a force due to the charge it induces on the wall of the cavity. If the point charge is not at the center of the sphere, it will exert a non-radial force on charges of opposite sign on the inner surface of the shell, which will redistribute to shield the charge and create a net force on the sphere. This force will pull the charge towards the wall of the shell and it will eventually spread uniformly over the outer surface. The electric field inside the metal is zero, but there can still be charge present on the inner and outer surfaces.
  • #1
ledin12
5
0
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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  • #2
No......
 
  • #3
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
 
  • #4
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.
 
  • #5
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.
 
  • #6
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]
 
  • #7
so that means charge is present on the inner and outer surface but not in the solid metal part.
Right?
 
  • #8
Exactly. The charge on the inner surface is -Q, the charge on the outer is +Q. In the metal the charge density is zero.
 
  • #9
I get it now. Thanks a lot!
 
  • #10
Glad to be of help,
Jano
 

1. What is a point charge in a conducting sphere?

A point charge in a conducting sphere refers to a small, localized charge placed at the center of a conducting sphere. The conducting sphere is a material that allows electrical charges to move freely within it, and the point charge creates an electric field within the sphere.

2. How does a point charge in a conducting sphere experience force?

A point charge in a conducting sphere experiences force due to the electric field created by the charge. The electric field exerts a force on the charge, causing it to move within the sphere.

3. What factors affect the force experienced by a point charge in a conducting sphere?

The force experienced by a point charge in a conducting sphere depends on the magnitude of the point charge, the distance between the point charge and the conducting sphere, and the properties of the conducting sphere (such as its size and charge distribution).

4. How is the force on a point charge in a conducting sphere calculated?

The force on a point charge in a conducting sphere can be calculated using Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this case, the charge on the conducting sphere and the distance between the point charge and the sphere's center must also be considered.

5. What are some real-world applications of a point charge in a conducting sphere experiencing force?

A point charge in a conducting sphere experiencing force can be used in various applications, such as in electrostatic generators, particle accelerators, and in the design of electronic circuits. It can also be used in experiments to study the behavior of electric fields and charges.

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