Integral of product of infintesimal volume

[vijaypandey93]

I'm following the book ''introduction to electrodynamics by D.J. Griffiths''. As he has written that the formula ''integral of product of infintesimal volume with the square of electric field'' gives us the energy contained in a charge configuration that is always positive because we're encountering square.He has justified it by saying that it even considers the fabrication of charges and as we know the fabrication of point charge involves infinite energy.But why do i get a definite value when i calculate the energy of a charge configuration like spherical or cylindrical,rather if I'm following his argument correctly then in spherical,this formula should take into account of fabrication of all the charges and that's certainly infinite.what's that in his argument that I'm not getting?Please help!

 

[Simon Bridge]

The energy stored in a charge configuration is the amount of work needed to get it into that state.
http://www.masteringphysicssolution...ions-energy-stored-in-a-charge-configuration/

Point charges are just models - all spherical charge distributions look like point charges from the outside.

 

[vijaypandey93]

okay but what'd we get if we calculate the energy due to equal and opposite charges?should it be positive or negative?according to the formula statrd above,it'll always be positive.and using the formula [k(q1)(q2)]/r,it's negative.can you please justify how?

 

[Simon Bridge]

Energy stored in an electric dipole.
https://www.physicsforums.com/showthread.php?t=260877


Also see:
https://www.physicsforums.com/showthread.php?t=631225

The work to get the + and - charges into position does not depend on how they got there (conservative force).
If you started with two neutral spheres, and moves positive charge from one to the other, you would have to do some work right?