A sample of paramagnetic salt contains `2.0 xx 10^(24)` atomic dipoles each of dipoles moment `1.5 xx 10^(-23) J T^(-1)`. The sample is placed under a homogeneous magnetic field of 0.64 T, and cooled to a temperature of 4.2K. 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)

Explanation

Here no. of dipoles `n = 2 xx 10^(24)`
Magnetic moment of each dipole `M = 1.5 xx 10^(-23)J T^(-1)`.
Total dipole moment of sample `= n xx M = 2 xx 10^(24) xx 1.5 xx 10^(-23) = 30`
As saturation achieved is 15% therefore, effective dipole moment
`M_(1) = (15)/(100) xx 4.5 J T^(-1), B_(1) = 0.64 T, T_(1) = 4.2 k`,
`M_(2) = ?, B_(2) = 0.98 T, T_(2) = 2.8 k`
According to Curie's law, `chi = C(M_(0))/(T) = (T)/(M)` or `I = (CH)/(T)`
As `I prop M` and `H prop B`
`:. M prop (CB)/(T), (M_(2))/(M_(1)) = (B_(2))/(B_(1)) = (T_(1))/(T_(2))`
or `M_(2) = (B_(2)T_(1)M_(1))/(T_(2)B_(1)) = (0.98 xx 4.2 xx 4.5)/(2.8 xx 0.64)`
`= M_(2) = 10.335 J T^(-1)`.