Question $2$

$[10]$

A ferrite magnet $($characteristic shown below$)$ is used as a source of flux for a magnetic door holder design as shown in the following diagram $($all dimensions in mm $).$ The magnet depth into the page is $20$ mm and all the soft steel pieces are assumed to have infinite permeability.

a$)$ Show that the dimensions, as given in the diagram, result in a plastic spacer flux density of about $0\mathrm{.}7$ T $.$ Assume for now that the plastic spacer is $0\mathrm{.}5$ mm long in the direction of the flux.

b$)$ For the given magnet dimensions, choose an appropriate thickness of the plastic spacer to limit the door opening force to $25$ N $.$

c$)$ A novel feature of this door opener is that when you press the button on the handle a short pulse of current flows through the $1500-$turn coil to disrupt the magnetic field and allow the door to be opened more easily. Determine how much current would be required to reduce the magnet flux to zero. Assume a spacer flux density of $0\mathrm{.}7$ T before pressing the button.