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# Machine riddle no.3 – Power generation in Mathematical city

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• #76
Hamid

Mayor of a mathematical city promised that electrical energy will be free for their future citizen, because they will consume no energy for electrical power generation!!

He said;” in our power plant, the generators start working with a little prime mover and produce a lot of electrical energy.”
He added our electrical generators will make a big permanent magnet that produces uniform magnetic field as generator stator and electrical windings that is located in its rotor, supplies load currents. The rotor of generator rotates within the gap without any energy consumption and produce required electromotive forces at end of windings although active/reactive consumers are connected to its terminals. Of course the electrical consumers shall be located in region of stator uniform magnetic flux.

He said, our mathematicians explain this technique as follow:
For integration of distributed forces on induced current elements we can write:
F = ∫ IB x dL where " I " is loads current, B is uniform magnetic flux density and " L " is electrical path that closed with electrical loads in region of uniform magnetic field.
Because of magnetic flux uniformity, we can write: F = -IB ∫ dL
Also the loop of electrical path is closed by loads; so we can write:
∫ dL = 0 and F = 0
Therefore in our power plant we will not need energy consumption for the electrical power producing.

What is your opinion? Is it possible?

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• #1192
Cheers,JSP

>For integration of distributed forces on induced >current elements we can write: >F = ? IB x dL where ” I ” is loads current, B is >uniform magnetic flux density and ” L ” is electrical >path that closed with electrical loads in region of >uniform magnetic field. >Because of magnetic flux uniformity, we can write: >F = -IB ? dL >Also the loop of electrical path is closed by loads; so >we can write: >? dL = 0 and F = 0 This is misleading. First of all arguing that the line integral of dL is zero because it is a closed path only makes sense for calculating the force on a charge moving in an electric field. It does not apply to a current in a wire in a magnetic field. Second, the current in a closed path will not be in the same direction inside the magnetic field so the net torque will be non zero. Think of a square loop; two sides of the loop will have zero torque on them and the other two sides will have opposite torques so they will add. Third, in some generators the B field is rotating and the load winding is stationary. The varying B field induces a voltage on the load winding. More turns gives more voltage. Stronger B gives more voltage. As the load increases, it takes more work to rotate the B field. If B does not vary, you don’t get any induced voltage. >What is your opinion? Tell the mayor to stick to poltics and let the sparky’s deal with the electricity. Cheers, JSP EE but not a PE

#1193
Hamid

Quote: Originally Posted by jsp “Second, the current in a closed path will not be in the same direction inside the magnetic field so the net torque will be non zero. Think of a square loop; two sides of the loop will have zero torque on them and the other two sides will have opposite torques so they will add.” Thank you very much, my dear friend, I think that portion of your sentences is correct completely. Indeed, the conclusion of F = ? IB x dL = 0 is not T = IS x B = 0 always.( T = Vector of angle torque and S = Vector of surface of closed induced current circuit) When you rotate the steering wheel of your car, the integration of forces that applied by your right and left hands to it is zero but the applied torque to it isn’t zero. THANKS

#1377
N P NAIR

Energy can neither be created nor be distroyed. Assuming a loss less system and assuming the rotor is rotating without any input, the rotor will slow down to a halt when external load is connected. This is because the load current will cause a retarding force on the rotor.

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