Saturday, August 10, 2019

homework and exercises - Two different solutions for the expression of potential energy of a uniformly charged solid sphere



I am a bit confused because I did some rigorous derivation of potential energy of a uniformly charged solid sphere and got two different solutions.(Sorry for the long exercise)


Now have a look at my 1st approach:- 1st approach in derivation of potential energy of uniformly charged solid sphere


I got the general result in my 1st approach which can easily be found in any textbook.


Now have a look at my 2nd approach:- 2nd approach in derivation of potential energy of a uniformly charged solid sphere


I got two different results and the second expression is numerically less than the first expression.I want to ask about this ambiguity of two different results for the same problem. I assumed the reference point to be infinity in both derivations and the solid spheres are non conducting.





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