25 Force and Torque from energy and co-energy

25 Force and Torque from energy and co-energy - Lecture 22...

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Lecture 22 Force and Torque from energy and co-energy We know from Lorentz’s law that the electromagnetic force is proportional to the cross product of the current and the magnetic field density f idl B ∝× . Form magnetically linear materials this force may be expressed as 1 2 T dL f ii dx = , where () Lxi λ = if x is translational displacement of the moving part or L i λθ = if θ is rotational displacement. In the latter case, the electromagnetic torque is 1 2 T Ti i d θ = Recall that the co-energy W φ ’ stored in the magnetic field is ' 1 , 2 T Wi i L i φ θθ = . Therefore the torque, for constant current, can be defined as ' . ic o n s t W T = = Also, since L i = , then 1 iL θλ = , and recalling that for linear devices the energy is equal to the co-energy, ' WW = , 1 , 2 T i L i = Substituting for λ , 1 1 1 1 , 2 1 , 2 TT WL L L  =  = and since L is symmetric, 1 1 , 2 T = Then the torque can also be calculated as
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This note was uploaded on 01/27/2011 for the course ECSE 361 taught by Professor Franciscodgaliana during the Spring '09 term at McGill.

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25 Force and Torque from energy and co-energy - Lecture 22...

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