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We have proved that the mutual imiuctance of coil 1 due to coil 2 are equal to the mutual inductance of coil 2 due to coil 1 {Lu = Ln = M). In a complicated situation {like this problem) that calculating the flux of one coil linkir'g to the other coil Heal is difcult. we can instead calculate the up\" and then calculate the mutual conductance. *lllllllllllllliillll h'M- '43\"th '- HF-hJ The figure shows a short solenoid l[II-Irith length l. radius a. and 11, turns per unit length} lies on the axis of a very long sotenoid [wi'l radius b, and n2 turns per unit length}. The short solenoid carries current i. We would like to determine the mutual inductance of these two ooils [Since the inner solenoid is short. it has a very complicated field, and it puts a different amount of flux through each turn of the long solenoid]. Instead we can assume that the current i is owing through the wire of the long solenoid and it is inducing on short solenoid. To nd the mutual inductance N. do these two steps: l {all Determine the magnetic ux density inside of a very long solenoid lb. "3. 1} using (a) Determine the magnetic flux density inside of a very long solenoid lb, n2. 1') using Ampere's law. (4 points) {bl Now assume that a short solenoid (a, \"1. ll lies inside of this long solenoid. Calculate the mutual inductance of these two solenoids. [5 points)