w=2c旧，6- -cge=r{c 2c2()d店 dEc佰 b)Energy Point of View n=v-0+e能 dt dt vdq=dWe +f:d=dWe vdq-fd -、w/ a=constant ;v=w 6q l=cons tant C dξ=0 f=0 Figure 11.6.2 Path of line integration in A Bξ state space (g,E)used to find energy at location C. Courtesy of Hermann A.Haus and James R.Melcher.Used with permission. 0 w。=-∫d+ vdq q=0 E=cons tant v=0 w.=c间 =cons tant q dq=2C(E) 1q2 f=-oW/ 1q2dc(5) g=constant 2 C2()dE v dc() d 6.641,Electromagnetic Fields,Forces,and Motion Lecture 12 Prof.Markus Zahn Page 2 of 96.641, Electromagnetic Fields, Forces, and Motion Lecture 12 Prof. Markus Zahn Page 2 of 9 ( ) ξ ξ ξ 1 1 2 2 dC W= C v , f = v 2 2 d ( ) ( ) ⎛ ⎞ − ⎜ ⎟ ξ ξ ξ ⎜ ⎟ ξ ⎝ ⎠ 2 2 2 1 q dC 1 d 1 = =q 2 d 2 dC C b) Energy Point of View ξ ξ + dq dWe d vi = v = f dt dt dt ξ ξ + ξ⇒ − ξ vdq = dW f d dW = vdq f d e e ξ = ξ= ∂ ∂ − = ∂ξ ∂ e e q cons tan t cons tan t W W f = ; v q Courtesy of Hermann A. Haus and James R. Melcher. Used with permission. 0 ξ = ξ= − ξ+ e ∫ ∫ q 0 cons tan t W = f d vdq ( ) ξ q v = C ( ) ( ) ξ = ξ ξ ∫ 2 e cons tan t q 1q W = dq = C C 2 (ξ) ξ 2 1 dC = v 2 d ( ) ( ) ( ) = ∂ ⎛ ⎞ ξ − − ⎜ ⎟ ∂ξ ξ ⎜ ⎟ ξ ξ ξ ⎝ ⎠ 2 e 2 2 q cons tan t W 1 d 1 1q dC f = = q = 2d 2 d C C