71. (a) We assume the current is changing at (nonzero) rate di/dt and calculate the total emf across both coils. First consider the coil 1. The magnetic ±eld due to the current in that coil points to the right. The magnetic ±eld due to the current in coil 2 also points to the right. When the current increases, both ±elds increase and both changes in ﬂux contribute emf’s in the same direction. Thus, the induced emf’s are E 1 = − ( L 1 + M ) di dt and E 2 = − ( L 2 + M ) di dt . Therefore, the total emf across both coils is E = E 1 + E 2 = − ( L 1 + L 2 +2 M ) di dt which is exactly the emf that would be produced if the coils were replaced by a single coil with inductance L eq = L 1 + L 2 +2 M . (b) We imagine reversing the leads of coil 2 so the current enters at the back of coil rather than the
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