Winding 1 in the loudspeaker of Problem 3.25 (Figure) is replaced by a permanent magnet as shown

Question:

Winding 1 in the loudspeaker of Problem 3.25 (Figure) is replaced by a permanent magnet as shown in Figure. The magnet can be represented by the linear characteristic B_m = ?_R (H_m ? H_c).

a. Assuming the voice coil current to be zero, (i₂ = 0), calculate the magnetic flux density in the air gap.

b. Calculate the flux linkage of the voice coil due to the permanent magnet as a function of the displacement x.

c. Calculate the co-energy W_fld?(i₂, x) assuming that the voice coil current is sufficiently small so that the component of W_fld due to the voice coil self inductance can be ignored.

d. Calculate the force on the voice coil.