Potential/Charge on Concentric Conducting Shells

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In summary, the conversation discusses a spherical capacitor with two thin metal spheres of different radii, and a series of operations that are completed. These operations include connecting the spheres with a wire, raising the outer sphere to potential +V, breaking the internal connection, and returning the outer sphere to ground potential. The question at hand is to determine the final potential and charge on the inner sphere. Based on Gauss' Law, it is determined that the inner sphere must have 0 charge and be at 0V with respect to ground after the operations are completed. The conversation ends with the confirmation that this reasoning is reasonable and accurate.
  • #1
blgeo
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I'm not 100% confident in my reasoning for this question because my answer seems unlikely:

Homework Statement



A spherical capacitor comprises two thin metal spheres of different radii but with
a common centre. The following series of operations is completed: The spheres are mutually connected by an internal wire. The outer sphere is raised to potential +V with respect to ground. The internal connection is broken. The outer sphere is returned to ground potential. Determine the final potential and the final charge on the inner sphere.


Homework Equations



Gauss' Law (integral form)

The Attempt at a Solution



As the spheres are connected by a wire initially I assume when the outer sphere is raised to V the inner sphere must be too. As they are at the same potential I think the charge on the inner sphere must be 0 at this point so that there is no field between the spheres (Gauss). When the connection is broken the inner sphere must then retain 0 net charge, and so when the outer sphere is returned to ground potential i think the inner sphere must have no charge and be at 0V with respect to ground.

This is the best argument I could come up with but I'm struggling to convince myself! Any help/confirmation of this answer would be appreciated
 
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  • #2
It sounds reasonable to me
 
  • #3
You can stop struggling now ... :approve:
 

FAQ: Potential/Charge on Concentric Conducting Shells

What is the concept of potential/charge on concentric conducting shells?

Potential/charge on concentric conducting shells refers to the distribution of electric charge and potential on two or more concentric spherical shells made of conducting material. It is an important concept in electrostatics that helps to understand the behavior of electric fields and charges in a system of concentric spheres.

How does the charge distribution on concentric shells affect the electric potential?

The charge distribution on the outer shell of a system of concentric conducting shells affects the electric potential at all points inside and outside the shells. The potential decreases as the distance from the outer shell increases, and it is constant within each shell. The inner shell carries no net charge and therefore does not contribute to the potential.

What is the equation for the potential on a concentric conducting shell?

The potential on a concentric conducting shell can be calculated using the following equation: V = kQ/r, where V is the potential, k is the Coulomb constant, Q is the total charge on the outer shell, and r is the distance from the center of the shells to the point where the potential is being measured.

How does the potential and charge on concentric shells change with distance from the center?

The potential on concentric shells decreases with distance from the center, while the charge remains constant on each shell. This is because the electric field is stronger closer to the outer shell, leading to a higher potential. The charge on each shell remains constant as it is evenly distributed over the surface of the shells.

How does the potential on concentric shells relate to the electric field between the shells?

The potential on concentric shells is directly proportional to the electric field between them. This means that as the potential decreases with distance from the outer shell, the electric field also decreases. This relationship is described by the equation E = -dV/dr, where E is the electric field, V is the potential, and r is the distance from the outer shell.

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