A loudspeaker is made of a magnetic core of infinite

A loudspeaker is made of a magnetic core of infinite

A loudspeaker is made of a magnetic core of infinite permeability and circular symmetry, as shown in figures a and b. The air-gap length g is much less than the radius r0 of the central core. The voice coil is constrained to move only in the x direction and is attached to the speaker cone, which is not shown in the figure. A constant radial magnetic field is produced in the air gap by a direct current in coil 1, il = I1. An audio-frequency signal i2 = I2 cos wt is then applied to the voice coil. Assume the voice coil to be of negligible thickness and composed of N2 turns uniformly distributed over its height h. Also assume that its displacement is such that it remains in the air gap (0 < x=””>< l=”” –=””>
a. Calculate the force on the voice coil, using the Lorentz Force Law (Eq. 3.1)
b. Calculate the self-inductance of each coil.
c. Calculate the mutual inductance between the coils. (Hint: Assume that current is applied to the voice coil, and calculate the flux linkages of coil 1. Note that these flux linkages vary with the displacement x.)
d. Calculate the force on the voice coil from the co-energyWfld.

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