Integral of product of infintesimal volume

AI Thread Summary
The discussion revolves around the integral of the product of infinitesimal volume and the square of the electric field, which is said to represent the energy in a charge configuration. While the formula suggests that energy should always be positive due to squaring the electric field, questions arise regarding the energy calculations for specific charge configurations, like spherical or cylindrical distributions. Participants highlight that point charges are models, and the energy associated with equal and opposite charges can yield conflicting results depending on the formula used. The work required to position charges is emphasized as independent of the method of charge placement, reinforcing the concept of conservative forces. Overall, the conversation seeks clarity on the apparent contradictions in energy calculations for different charge arrangements.
vijaypandey93
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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!
 
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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?
 
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