G9 - A>9 H=-0Ψ= 0z -盯 -<2 -d/2 d/2 IV.Toroidal Coil toroid axis N:turns Figure 9.4.1 Toroidal coil with Figure 9.4.2 Surface S donut-shaped magnetizable core. enclosed by contour C used with Ampere's integral law to determine H in the coil shown in Figure 9.4.1. Courtesy of Hermann A.Haus and James R.Melcher.Used with permission. 6.641,Electromagnetic Fields,Forces,and Motion Lecture 8 Prof.Markus Zahn Page 6 of 136.641, Electromagnetic Fields, Forces, and Motion Lecture 8 Prof. Markus Zahn Page 6 of 13 ⎧ ⎫ ⎪ ⎪ ⎛ ⎞ − + ⎜ ⎟ − ⎝ ⎠ ⎨ ⎬ − > ⎪ ⎪ ⎡ ⎤⎡ ⎤ ⎛⎞ ⎛⎞ ⎢ ⎥⎢ ⎥ +− ++ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ ⎩ ⎭ ⎣ ⎦⎣ ⎦ 0 1 1 2 2 2 2 2 2 d d z z M 2 2 d z 2 2 d d Rz Rz 2 2 ⎧ ⎫ ⎪ ⎪ ⎛ ⎞ − + ⎜ ⎟ − ⎝ ⎠ ⎨ ⎬ − + − << ⎪ ⎪ ⎡ ⎤⎡ ⎤ ⎛⎞ ⎛⎞ ⎢ ⎥⎢ ⎥ +− ++ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ ⎩ ⎭ ⎣ ⎦⎣ ⎦ 0 1 1 2 2 2 2 2 2 d d z z M 2 2 d d 2 z 2 22 d d Rz Rz 2 2 IV. Toroidal Coil Courtesy of Hermann A. Haus and James R. Melcher. Used with permission. −∂ Ψ ∂ H= = z z N1 turns