What is the Energy of a Charged Sphere of Radius R?

In summary, the conversation discusses finding the potential inside a sphere with charge density kr, and calculating the energy of the configuration by integrating rho*phi/2 over the volume of the sphere. The origin of the energy is explained as the work done in configuring the sphere, and the final answer is calculated to be 35pi^2k^2R^7/72 or 4pi*k^2*R^7/21*epsilon. The speaker is unsure of the correctness of their answer and asks for confirmation.
  • #1
heman
361
0
A sphere of radius R carries a charge density kr(where k is a constant!).What will be the energy of the Configuration??
 
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  • #2
1. Find the potential phi(r) inside the sphere.
2. Integrate rho*phi/2 over the volume of the sphere.
3. The algebra is a bit complicated. I get 35pi^2k^2R^7/72, but check me for errors.
 
  • #3
Gentleman,Why won't will be find the Potential outside the sphere..
I am very much perplexed with this Energy term..This is interaction energy
Pls help logically,i can do the maths involved.!
Pls explain the origin of energy and i think we will integrate over whole space...but i don't have clear idea.!
 
  • #4
Meir Achuz said:
1. Find the potential phi(r) inside the sphere.
2. Integrate rho*phi/2 over the volume of the sphere.
3. The algebra is a bit complicated. I get 35pi^2k^2R^7/72, but check me for errors.


Well i got the solution as 4pi*k^2*R^7/21*epsilon!
I don't know whether you are correct or me!
 
  • #5
The energy is due to the work done in configuring the sphere. Consider the sphere of radius r, and add a layer of thickness dr. Calculate the work dw is required to put this layer of charge. Integrate the work dw over the radius 0 to R. This will be the energy of the configuration
 

What is energy of configuration?

Energy of configuration refers to the energy stored in a system due to its position or arrangement. It is the potential energy of a system caused by its physical or chemical structure.

How is energy of configuration calculated?

The calculation of energy of configuration depends on the type of system. For example, in a mechanical system, it can be calculated using the equation E = 1/2kx^2, where k is the spring constant and x is the displacement. In a chemical system, it can be calculated using the bond dissociation energy of the molecules involved.

What factors affect energy of configuration?

The factors that affect energy of configuration include the type of system, the position or arrangement of the components, and any external forces or interactions. For example, in a mechanical system, the strength of the spring and the displacement of the object will affect its energy of configuration.

Why is energy of configuration important?

Energy of configuration is important because it is a fundamental concept in understanding and predicting the behavior of physical and chemical systems. It helps explain the stability, changes, and interactions of systems, and is crucial in various fields such as engineering, physics, and chemistry.

How can energy of configuration be changed?

Energy of configuration can be changed by altering the position or arrangement of the components in a system. This can be done by applying external forces, such as mechanical work or heat, or by changing the chemical structure through reactions. The amount of energy of configuration can also be influenced by changing the properties of the system, such as the strength of bonds or the elasticity of materials.

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