The cross-section of a two-dimensional cylindrical system is shown in Fig. P9.6.3. A region of…

The cross-section of a two-dimensional cylindrical system is shown in Fig. P9.6.3. A region of free space having radius e787eb03 384f 4286 8f79 f676ae475002 is surrounded by material having permeability 945d6c0e 7bf0 40e1 ae9b d687441ba468 which can be considered as extending to infinity. A winding at 2b7cc8d8 261e 4857 aa2a d98201bde8c9 is driven by the current c90dfe3b 962a 49fc a2f4 4d7c5d556369 and has turns density 379d16b1 5444 48c8 9e87 0c49eea26dba sin φ (turns per unit length in the φ direction). Thus, at 2b7cc8d8 261e 4857 aa2a d98201bde8c9, there is a current density 892a7092 0902 471e 8c19 b4cc3bb2cb8c

Fig. P9.6.3

3da745cd bbdc 4611 9d9d 2b7e15649594

(a) show that

17707409 791e 4eda ac1c d766c234b7a1

(b) An n-turn coil having a spacing between conductors of 2a is now placed at the center. The magnetic axis of this coil is inclined at the angle α relative to the cd471cc5 1487 44f8 98ec ada79eef98a5 axis. This coil has length 398112ea 1490 4976 83c3 cbed406fcd2d in the 9818f17f 15b5 4f0c bd95 2842bdba8351 direction. Show that the mutual inductance between this coil and the one at 1e96610d 3652 45da aaee 4724d49e04f3

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