Charge on two concentric spherical shells

In summary, the conversation discusses a system of two concentric spherical shells connected to a battery. The question is whether the system will become stable and if the charges on the spheres will remain static. It is suggested that the system may act as a capacitor and the amount of charges on the spheres would be the same. However, there is uncertainty about the stability of the system due to the difference in charge density on the spheres. The concept of charge conservation is mentioned and the definition of stability is questioned.
  • #1
brianeyes88677
13
0
There are two spherical shells in different sizes and they are concentric. Now if I connect a battery to the two spheres (connect the negative pole to the smaller sphere and connect the positive pole to the bigger sphere). Will this system become stable? Or is there any situation for the charges on these spheres stay static?
 
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  • #2
brianeyes88677 said:
Will this system become stable?
Sure. Do you expect something else?
You are connecting a battery to a capacitor (assuming the shells are conducting).
 
  • #3
If it is a capacitor then what's the ratio of the amount of charges on the both sphere? (the radii are r and R)
 
  • #4
Is this homework? If yes, please post the full problem statement and your work so far.

What do you think?
 
  • #5
This is not a homework, it's just a concept that flash through my mind. If it is a capacitor just like you say, the amount of charges on the two spheres should be the same, but I think this isn't reasonable, how can it be stable if the amount of charges are the same?
 
  • #6
brianeyes88677 said:
This is not a homework, it's just a concept that flash through my mind. If it is a capacitor just like you say, the amount of charges on the two spheres should be the same
Yes, this is given by charge conservation.
brianeyes88677 said:
how can it be stable if the amount of charges are the same?
Where is the problem?
 
  • #7
No, the system will not become stable because the smaller sphear has shaper edges, charges are more concentrated on sharper surfaces(smaller spheare).
 
  • #8
Wait, what is meant by "stable" here? In terms of electric charge distribution, or in terms of forces if we don't have supports? I assumed the former one, where the different charge density is not an issue.
 

FAQ: Charge on two concentric spherical shells

What is the equation for finding the charge on two concentric spherical shells?

The equation for finding the charge on two concentric spherical shells is Q = (4πε0)(R1 - R2)Φ, where Q is the total charge, ε0 is the permittivity of free space, R1 is the radius of the larger shell, R2 is the radius of the smaller shell, and Φ is the electric flux through the region between the two shells.

How does the charge distribution on the two shells affect the electric field between them?

The charge distribution on the two shells affects the electric field between them by creating a radial electric field that points from the larger shell to the smaller shell. The magnitude of the electric field is directly proportional to the charge on each shell and inversely proportional to the distance between them.

What happens to the electric field if the two shells have the same charge?

If the two shells have the same charge, the electric field between them will be zero. This is because the electric fields created by each shell will cancel each other out, resulting in a net electric field of zero.

Can the charge distribution on the two shells be different and still have a net electric field of zero?

Yes, it is possible for the charge distribution on the two shells to be different and still have a net electric field of zero. This can occur if the smaller shell has a higher charge density than the larger shell, resulting in a stronger electric field from the smaller shell that cancels out the electric field from the larger shell.

How does the distance between the two shells affect the charge on each shell?

The distance between the two shells does not directly affect the charge on each shell. However, as the distance between the two shells increases, the electric field between them decreases, which can result in a redistribution of charge on the two shells. This is because the charges on the shells will repel each other and move to positions that result in a lower overall electric field between them.

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