Breaking & building a charged hollow sphere

In summary, the problem involves a charged hollow sphere with surface charge density \sigma and radius R being cut into two hemispheres. These hemispheres, with equal charges on them, would repel each other. To align them back to their original state, a force needs to be applied on both hemispheres. The repulsive force can be calculated using Coulomb's law if they are considered as point charges. The charge distribution of the hemispheres will change once they are separated.
  • #1
xxhizors
6
0
A charged hollow sphere with surface charge density [itex]\sigma[/itex] & radius R is cut into two hemispheres...certainly the hemispheres with equal charges on them would repel each other...Now a force is applied on both the hemispheres to align them again as the original sphere..i shall be highly thankful if u could assist me finding that force applied on each hemisphere...its not a homework assignment...just a question i saw in a book...!
 
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  • #2
xxhizors said:
A charged hollow sphere with surface charge density [itex]\sigma[/itex] & radius R is cut into two hemispheres...certainly the hemispheres with equal charges on them would repel each other...Now a force is applied on both the hemispheres to align them again as the original sphere..i shall be highly thankful if u could assist me finding that force applied on each hemisphere...its not a homework assignment...just a question i saw in a book...!

Welcome to the PF.

Interesting problem. If they were point charges, what would be the repulsive force as a function of separation discance? Once the two hemispheres are no longer in contact, what will the (formerly uniform) charge distribution be?
 
  • #3
How can we consider them as point charges in this problem...??
The repulsive force between the point charges can be calculated from coulomb's law...
I thought this about approaching this problem..

let us take a hemisphere & we try to build another on it and see the force of repulsion due to each infinitely small ring constituting the upper hemisphere on the lower one...
i can consider hemisphere to be build from infinite rings...
 

1. What is a charged hollow sphere?

A charged hollow sphere is a spherical object with a hollow interior that has a net electric charge. This means that the total amount of positive and negative charges within the sphere are not equal, resulting in an overall charge.

2. How is a charged hollow sphere created?

A charged hollow sphere can be created by either transferring electrons to or from the surface of a neutral hollow sphere, or by charging a non-conductive hollow sphere through induction using a charged object.

3. What happens when a charged hollow sphere is broken?

When a charged hollow sphere is broken, the resulting pieces will have the same amount of charge as the original sphere, but the distribution of the charge will be different. The broken pieces will also have their own electric fields.

4. How is a charged hollow sphere built?

A charged hollow sphere can be built by either transferring electrons to or from the surface of a neutral hollow sphere, or by charging a non-conductive hollow sphere through induction using a charged object. The amount and distribution of the charge can be controlled by the method used to charge the sphere.

5. What are some real-life applications of a charged hollow sphere?

A charged hollow sphere has various applications in technology and research. For example, it can be used in particle accelerators to create and manipulate charged particles, in electrostatic generators to produce high voltages, and in electrostatic precipitators to remove impurities from industrial exhaust. It is also a fundamental concept in understanding the behavior of electric fields and charges.

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