1 dL() d II.Force on a Wire over a Perfectly Conducting Plane Depth D 00 Figure 11.7.3 Cross-section of perfectly conducting current-carrying wire over a perfectly conducting ground plane. Courtesy of Hermann A.Haus and James R.Melcher.Used with permission. [See Haus Melcher p.343, take 12 of Eq.(12)which is the inductance between 2 cylinders] A.Energy Method 专r但0 1 de 4πR )-1 f。 Figure 11.7.4 The force tending to levitate the wire of Figure 11.7.3 as a 2 3 function of the distance to the ground plane ξ/R- normalized to the radius R of wire. Courtesy of Hermann A.Haus and James R.Melcher.Used with permission. 6.641,Electromagnetic Fields,Forces,and Motion Lecture 13 Prof.Markus Zahn Page 3 of 146.641, Electromagnetic Fields, Forces, and Motion Lecture 13 Prof. Markus Zahn Page 3 of 14 ( ) ( ) 2 2 1 1 dL = 2 d L ⎛ ⎞ ξ −λ−⎜ ⎟ ξ ξ ⎝ ⎠ ( ) 2 1 dL i 2 d ξ = ξ II. Force on a Wire over a Perfectly Conducting Plane Courtesy of Hermann A. Haus and James R. Melcher. Used with permission. ( ) 2 0D L = ln 1 2 RR ⎡ ⎤ µ ξ ξ ⎛ ⎞ ξ +− ⎢ ⎥ ⎜ ⎟ π ⎝ ⎠ ⎣ ⎦ A. Energy Method ( ) ( ) 2 2 0 2 1 1 dL i D f= i = 2 d 4R 1 R ξ ξ µ ξ π ξ − [See Haus & Melcher p. 343, take ½ of Eq. (12) which is the inductance between 2 cylinders] Courtesy of Hermann A. Haus and James R. Melcher. Used with permission. Depth D