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

Here, no. of dipoles, `n=2xx10^(24)`
Magnetic moment of each dipole, `M^'=1.5xx10^(-23)JT^-1`
Total dipole moment of sample`=nxxM^'=2xx10^(24)xx1.5xx10^(-23)=30JT^-1`
As saturation achieved is `15%`, therefore effective dipole moment
`M_1=15/100xx30=4.5JT^-1`, `B_1=0.64T`, `T_1=4.2K`
`M_2=?` `B_2=0.98T`, `T_2=2.8K`.
According to Curie's law, `chi_m=C/T=1/H` or `I=(CH)/(T)`
As `IpropM` and `HpropB` `:. Mprop(CB)/(T)`,
`(M_2)/(M_1)=B_2/B_1*T_1/T_2` or `M_2=(B_2T_1M_1)/(T_2B_1)=(0.98xx4.2xx2.5)/(2.8xx0.64)`, `M_2=10.34JT^-1`