A toroidal solenoid with mean radius r and cross sectional area A is wound unifo

Question

A toroidal solenoid with mean radius r and cross sectional area A is wound uniformly with N1 turns. A second toroidal solenoid with N2 turns is wound uniformly on top of the first, so that the two solenoids have the same cross-sectional area and mean radius.

What is the mutual inductance of the two solenoids? Assume that the magnetic field of the first solenoid is uniform across the cross section of the two solenoids. Express your answer in terms of the variables N1, N2, A, r, magnetic constant u0 and other appropriate constants.

If N1 = 550 turns, N2 = 260 turns, r = 10.8cm and A = 0.68cm^2, what is the value of the mutual inductance? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

Mutual Inducatance is given by

M= u0 * N1 * N2 * A /(2Pi*r)

u0 = permeability...=4Pi*10^-7

Area = 0.68 cm^2 = 0.68 *10^-4 m^2

r =10.8cm = 0.108 m

M = 4Pi*10^-7 * 550 * 260 * 0.68*10^-4 / 0.108 = 1.80*10^-5 H..

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