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A sample of paramagnetic salt contains 2.0 xx 10^(24) atomic dipoles each of dipole moment 1.5 xx 10^(-23) J T^(-1) . The sample is placed under a homogeneous magnetic field of 0.64 , and cooled to a temperature of 4.2 K . The degree of magnetic saturation achieved is equal to 15% . What is the total dipole moment of the sample for a magnetic field of 0.98 T and a temperature of 2.8 K? |
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Answer» SOLUTION :Here number of atomic dipole `N = 2.0 XX 10^(24)`, magnetic moment of each dipole `m = 1.5 xx 10^(-23) J T^(-1)` . If degree of magnetic saturation be F, then total magnetic moment `m_0 = N m f` As at T = 4.2 K and B = 0.84 T, f = 15% = 0.15 , hence applying Curie.s law `m_0 = (CB)/(T)` , we have `C = (m_0 T)/(B) = (N m f T)/(B) = (2.0 xx 10^(24) xx 1.5 xx 10^(-23) xx 0.15 xx 4.2)/(0.64) = 22.5` Then for `T. =2.8 K ` and B.= 0.98 T, the total dipole moment of the sample will be `m._0 = (CB.)/(T.) =(22.5xx0.98)/(2.8) =7.88 A m^2` . |
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