Two circular planar coils that have 300 and 360 loops, respectively, and corresp

Question

Two circular planar coils that have 300 and 360 loops, respectively, and corresponding radii of 0.27 m and 0.39 m share a common axis with the coil centers separated by 7.2 m and with the axis perpendicular to both planes of the coil. The permeability of free space is 4 pi times 10-7 N/A2. What is the mutual inductance of the coils? Hint: Use the far-field approximation. Answer in units of H. If coil 2, carrying a constant current 25 A, is moving at a velocity of 34 m/s along the axis, what is the magnitude of the cmf induced in coil 1 when the distance between them is 7.2 m? Answer in units of V.

Explanation / Answer

Mutual inductance of the coils is M = pi * uo * N1 * N2 * R2^2 / 2R1 = 3.14 * (4 * 3.14 * 10^-7) * (300) * (360) * (0.39)^2 / 2 * 0.27 = 0.1199 H Emf = e = M * di/dt = 0.1199 * 25 / (34 / 7.2) = 0.6351 V

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