A sample of paramagnetic salt contains `2xx10^(24)` atomic dipoles, each of moment `1.5xx10^(-23)JT^-1`. The sample is placed under a homogeneous magnetic field of `0.64T` and cooled to a temperature of `4.2K`. The degree of magnetic saturation archieved is equal to `15%`. What is the total dipole moment of the sample for a mangetic field of `0.98T` and a temperature of `2.8K`. (Assume Curie's law).

Explanation

Number of atomic edipoles n=2.0xx`10^(24)`
Dipole moment of each atomic dipole, `M=1.5xx10^(-23)JT^(-1)`
When the magnetic field, `B_(1)=0.64T`
The sample is cooled to a temperature, `T_(1)=4.2^(@)K`
Total dipole moment of the atomic dipole, `M_("tot")=nxxM`
`=2xx10^(24)xx1.5xx10^(-23)`
=30J`T^(-1)`
Magnetic saturation is acheived at 15%
`M_(!)=(15)/(100)xx30=4.5J T^(-1)`
Hence, effective dipole moment,
when the magnetic field `B_(2)=0.98T`
temperature `T_(2)=2,8^(@)K`
Its total dipole moment`=M_(2)`
According to Curie's law, we have the ratio of two magnetic dipoles as:
`(M_(2))/(M_(1))=(B_(2))/(B_(1))xx(T_(1))/(T_(2))`
` therefore M_(2)=(B_(2)T_(1)M_(1))/(B_(1)T_(@))`
`=(0.98xx4.2xx4.5)/(2.8xx0.64)=10.336J T^(-1)`
Therefore, 10.336 `J T^(-1)` is the toal d ipole moment of the sample for a magnetic field of 0.98T and a temperature of 2.8J,