Concept/Derivation for total electric potential energy of two concentric spheres

Sumedh

What will be the total electric potential energy of two concentric spheres.

Will it be
= [P.E. of Inner sphere] + [ P.E. of Outer sphere] + [ Energy required to bring outer sphere from infinity to the present position(i.e. position concentric to inner sphere) ]


OR it


Will it be
= [P.E. of Inner sphere] + [ P.E. of Outer sphere] + [ Energy required to bring outer sphere from infinity to the present position(i.e. position concentric to inner sphere) ]
+[ Energy required to bring inner sphere from infinity to the present position(i.e. position concentric to outer sphere sphere) ]

clem

PE=(1/2)[Q1 V1 + Q2 V2], where V1 is potential on sphere 1 due to both spheres.
This is for conducting spheres. If not conducting, you have to integrate over eadh surfqce.

Sumedh

Thank you very much, I got it