Figure shows the magnetic circuit for a permanent-magnet loudspeaker. The voice coil (not shown) is in the form of a circular cylindrical coil which fits in the air gap. A samarium-cobalt magnet is used to create the air-gap dc magnetic field which interacts with the voice coil currents to produce the motion of the voice coil. The designer has determined that the air gap must have radius R = 1.8 cm, length g = 0.1 cm, and height h = 0.9 cm. Assuming that the yoke and pole piece are of infinite magnetic permeability (? ? ?), find the magnet height hm and the magnet radius Rm that will result in an air-gap magnetic flux density of 1.2 T and require the smallest magnet volume.

. Air gap Pole Yoke piece Magnet Ra