Suppose the needle in Problem 106 is a uniformly magnetized iron rod that is 8 cm long and has a cross-sectional area of 3 mm². Assume that the magnetic dipole moment for each iron atom is 2.2?_B and that all the iron atoms have their dipole moments aligned. Calculate the frequency of small oscillations about the equilibrium position when the magnetic field is 0.5 G.

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Magnetic Susceptibility of Materials at 20C Various Material X m 2.3 x 10 5 Aluminum -1.66 x 10-5 Bismuth Copper Diamond -0.98 x 10-5 -2.2 x 10-5 Gold -3.6 x 10-5 1.2 x 10-5 -3.2 x 10-5 Magnesium Mercury Silver -2.6 x 10-5 Sodium -0.24 x 10-5 Titanium 7.06 x 10-5 Tungsten Hydrogen (I atm) 6.8 x 10-5 -9.9 x 10-9 Carbon dioxide (1 -2.3 x 10-9 atm) Nitrogen (1 atm) -5.0 x 10-9 Oxygen (1 atm) 2090 x 10-9