Magnetic fields are commonly produced in air-gaps of magnetic yokes. The magnitude of the field is commonly controlled by winding currents. An example is the blue magnetic yoke shown, which

is used to produce a uniform magnetic field in the air-gap between the two black poles. The large circular"wheels" are actually water cooled windings, with N turns,carrying a large amount of current. The magnetic circuit for this device is shown below. For this device, the cross section ofthe core has dimensions: A = 2.5 in × 5 in. The total length magnetic core of the core (around the entire perimeter) is l. = 48 inches. The windings are wrapped around the arms of the core. Each winding has N turns and carries the same current, I. The current flow through both windings such that the magnetic flux they produce flows left-to-right. The cross section of the arms is circular and has a diameter of 3 inches. The length of the arm is 4.5inches. Both the core and the arms have permeability µ=1500µ,. The length of air gap is l =windings3 inches, and can be assumed to have the same cross-sectional area as the arms (this neglects field fringing). If both windings carry a current of 30 amps, determine the number of turns of each winding such that the flux density produced in the air gap region is B, =1 Wb/m²