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.

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