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6.641,Electromagnetic Fields,Forces,and Motion Prof.Markus Zahn Lecture 13:Magnetoquasistatic Forces I.MQS Energy Method of Forces V= dx dt (b) (a)Magnetoquasistatic system having one electrical terminal pair and one mechanical degree of freedom.(b)Schematic representation of MQS subsystem with coupling to external mechanical system represented by a mechanical terminal pair. A.Circuit Approach v-0-品(0-L(e+9 dt p=i=L()+包 dt -L6{ =2(r小r9 =2ge i-0+5w=(0P,专=图 dt d =L=5-围 、d 6.641,Electromagnetic Fields,Forces,and Motion Lecture 13 Prof.Markus Zahn Page 1 of 146.641, Electromagnetic Fields, Forces, and Motion Lecture 13 Prof. Markus Zahn Page 1 of 14 6.641, Electromagnetic Fields, Forces, and Motion Prof. Markus Zahn Lecture 13: Magnetoquasistatic Forces I. MQS Energy Method of Forces A. Circuit Approach () () λ (ξ) ⎡ ⎤ ξ ξ+ ⎣ ⎦ d d di dL v= = L i =L i dt dt dt dt ( ) (ξ) ξ + 2 di dL p = vi = L i i dt dt ( ) ( ) 2 2 d 1 dL =L i i dt 2 dt ⎛ ⎞ ξ ξ + ⎜ ⎟ ⎝ ⎠ ( ) ( ) 2 2 d1 1 dL = Li i dt 2 2 dt ⎡ ⎤ ξ ξ + ⎢ ⎥ ⎣ ⎦ ( ) ( ) 2 2 d1 1 d dL = Li i dt 2 2 d dt ⎡ ⎤ ξ ξ ξ + ⎢ ⎥ ⎣ ⎦ ξ ( ) ( ) m 2 2 m dW d1 1 dL vi= f W = L i , f = i dt dt 2 2 d ξ ξ ξ ξ +⇒ ξ ξ ( ) ( ) ξ ξ λ ξ⇒ ξ 2 1 dL =L i f = i 2 d
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