Figure E12.1.1 can also be considered as a simple model of a magnetically operated relay that is commonly used for the automatic control and protection of electric equipment. Consider the core and armature (shown as "Bar" in Figure E12.1.1) of the relay to be constructed out of infinitely permeable magnetic material. The core has a circular cross section and is 1.25 cm in diameter, while the armature has a rectangular cross section. The armature is so supported that the two air gaps are always equal and of uniform length over their areas. A spring (not shown in the figure), whose force opposes the magnetic pull, restrains the motion of the armature. If the operating coil has 1800 turns carrying a current of 1 A, and the gaps are set at 0.125 cm each, find the pull that must be exerted by the spring. You may neglect leakage and fringing.
