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Conceptual Questions No.3- Missed Energy
Let's imagine the year 2107.In that time electrical power will be generated in nuclear power plants and electrical energy will be produced in big nuclear reactors.Also the electrical energy will be transmitted by superconductor cables.
This conceptual question is subjected to one of transmission line projects which intended by power plant owner (client).According to project technical documents, the contractor shall approach one of two DC transmission lines to other line (equal to "d" meter) without lines deenergizing.After that mentioned displacement, the cross distance of two lines changes from "d" meter to zero meter.
At the end of works, the representative of client who is electrical engineer shall account the amount of money that shall be paid to contractor.
He must estimate amount of done works by them. According to fundamental electromagnetic theory for enclosed energy estimation in one meter of transmission lines, he can write:

                                             W=1/2∫volB.H dv

Also:                              i = ∫H. dl = H 2πr

and                           dv = 2πr dr

                       W = 1/2∫volB.H dv = 1/2∫0d B.i/2πr× 2πr dr

Consequently, calculated done works by client are :
                                       W = 1/2∫0d B.i dr      

But the representative of contractor who is mechanical engineer thinks above mentioned calculation is not right and client shall be paid more money for done works.
According to fundamental mechanical theory, the representative of contractor tries to do calculation by the other way. He writes:

                                              W =∫L F.dr

                                                 F = i x B

                                   W= ∫0d Bidr

Consequently, done works calculated by contractor are:
                                              W= ∫0d Bidr      

Therefore amount of done works calculated by contractor are two time of client estimated.

What is your opinion? Who is right?
Author : Hamid - From: Iran
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