Question 5.23: A sample of paramagnetic salt contains 2.0 × 10 24 atomic dipoles each of dipole moment 1.5 × 10 −23 J T −1 . The sample is placed under a homogeneous magnetic field of 0.64 T, 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? (Assume Curie’s law)Class 12 - Physics - Magnetism And Matter Magnetism And Matter Page-203

Question 5.23: A sample of paramagnetic salt contains 2.0 × 10 24 ato

1.	Question 5.23: A sample of paramagnetic salt contains 2.0 × 10 24 atomic dipoles each of dipole moment 1.5 × 10 −23 J T −1 . The sample is placed under a homogeneous magnetic field of 0.64 T, 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? (Assume Curie’s law)Class 12 - Physics - Magnetism And Matter Magnetism And Matter Page-203
Answer» Number of ATOMIC dipoles, n = 2 × 10²⁴ dipole of each dipole MOMENT ,M = 1.5 × 10^-23J/T so, dipole moment at complete SATURATION, M = 2 × 10²⁴ × 1.5 × 10^-23 = 30 J/T at 0.84T and 4.2K , 15% of sample is magnetised. so use FORMULA, $M=C\frac{B_0}{T_0}\\\\15\:of\:30J/T=C\frac{0.84}{4.2}$ ----(1) at 0.98T and 2.8K , $M=C\frac{0.98}{2.8}$ -----(2) from equations (1) and (2), M = 7.875 J/T

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