# Energy of Configuration

A sphere of radius R carries a charge density kr(where k is a constant!).What will be the energy of the Configuration??

Meir Achuz
Homework Helper
Gold Member
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!

mukundpa
Homework Helper
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