(Solved): Answer should be as follows: Voice coil actuators 5.21 Voice coil actuator. A cylindrical voice coil ...

Voice coil actuators 5.21 Voice coil actuator. A cylindrical voice coil actuator is shown in Figure 5.108. A permanent magnet, magnetized radially, is placed on the outer surface of the gap with a free moving coil on the inner cylinder that can move back and forth. The mass of the coil is $m=50\mathrm{g}$, the current in the coil has amplitude $I=0.4$ A and frequency $f=50\mathrm{Hz}$, the number of turns in the coil is $N=240$, and the magnetic flux density due to the permanent magnet is $B=0.8\mathrm{T}$. The coil has an average diameter of $22.5\mathrm{mm}$. This device is used as a positioner or as the drive in a vibrating pump. The activating mechanism is connected directly to the coil. (a) Calculate the force on the coil. (b) If the cylinder has a restoring constant $k=250\mathrm{N}/\mathrm{m}$ (provided by a spring), calculate the maximum displacement of the moving piece. (c) Calculate the maximum acceleration of the coil/cone assembly. Figure 5.108 A voice coil actuator. The magnetic field is indicated by the vertical arrows 5.21 (a) $5.43\mathrm{N}$. (b) $21.7\mathrm{mm}$. (c) $108.6\mathrm{m}/{\mathrm{s}}^2$.