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

AI Thread Summary
The discussion centers on calculating the energy of a charged sphere with a charge density of kr. Participants explore finding the potential phi(r) inside the sphere and integrating the energy density over its volume. One contributor initially calculates the energy as 35pi^2k^2R^7/72, while another arrives at a different result of 4pi*k^2*R^7/21*epsilon. The energy is explained as the work required to assemble the charge configuration layer by layer. The conversation highlights the complexities of the algebra involved and the need for clarity in integrating over the entire volume.
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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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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.
 
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.!
 
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!
 
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
 

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