(Solved): 5.22 Voice coil actuator. A voice coil actuator used for positioning purposes is built as shown in ...

5.22 Voice coil actuator. A voice coil actuator used for positioning purposes is built as shown in Figure 5.109. Two pairs of magnets produce uniform magnetic flux densities of $0.8\mathrm{T}$ in the space between each pair. In the left pair, the flux density points up whereas in the right pair it points down. A rectangular coil, $65\mathrm{mm}$ wide and $50\mathrm{mm}$ deep with $N=250$ turns, is placed between the magnets, shown in its rest position centered between the magnets. The actuator is used to position a device (not shown) in the limits $x\pm 20\mathrm{mm}$ from the rest position by applying appropriate currents in the coil. Given the dimensions shown and mass of the coil $m=10\mathrm{g}$ find: (a) The velocity of the coil as a function of its position $x$ and current $I$. (b) Time needed for the coil to reach its extreme position for a maximum coil current of $100\mathrm{mA}$. (c) Maximum acceleration of the coil. Figure 5.109 A voice coil actuator Answers to the problem are show below, please only answer if you are able to obtain these solutions, thank you! (a) $v=\sqrt{4000Ix}[\mathrm{m}]$. (b) $14.1\mathrm{ms}$. (c) $200\mathrm{m}/{\mathrm{s}}^2$.