19 Force and Torque 1

19 Force and Torque 1 - Lecture 21 Force and Torque Given a...

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Lecture 21 Force and Torque Given a system of initially coupled coils with a moving part () Lxi λ = , where x is the position of the moving part, then by the first law of thermodynamics, elec mech WW W φ ∆= + If x changes by x at constant current i then, 1 2 T Wi L i where L Lx x Lx + ∆− . In addition the electric energy delivered by the n external sources during the change can be obtained as, TT elec d i = where L xx i L x i + ∆ − . Then 1 2 T mech elec W i L i = Let us consider an infinitesimal change x dx ∆→ , and then the differential of the energy would be mech elec dW dW dW =− If additionally we consider a differential of the current (no longer constant) then the differential of the stored energy in the field is 11 22 T T dW i di L x dx i i L x i =+ + + T T T dW i L x dx i di L x dx i i L x dx di di L x i L x i  = + ++ + +  Since T L xd x L xd x += + then d iLx d xi iLx d i + . The last term within the brackets can be neglected since it involves differentials squared. We can therefore
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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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19 Force and Torque 1 - Lecture 21 Force and Torque Given a...

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