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
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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,
----(1)
at 0.98T and 2.8K ,
-----(2)
from equations (1) and (2),
M = 7.875 J/T
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,
at 0.98T and 2.8K ,
from equations (1) and (2),
M = 7.875 J/T
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