A paramagnetic sample shows a net magnetisation of `8Am^-1` when placed in an external magnetic field of `0*6T` at a temperature of `4K`. When the same sample is placed in an external magnetic field of `0*2T` at a temperature of `16K`, the magnetisation will be

Options

A. `(32)/(3)Am^(-1)`
B. `(2)/(3)Am^(-1)`
C. `6Am^(-1)`
D. `2.4Am^(-1)

Answer

A

Explanation

`Here, M_(1)=8Am^(-1), B_(1)=0.6T`
`T_(1)=4K, B_(2)=0.2T, T_(2)=16K`
Then, for paramagnetic materials,
magnetisation(M)=`C(B)/(T)("Curie's law")`
Now, in the first case, `M_(1)=(CB_(1))/(T_(1))……(i)`
and in the second case, `M_(2)=(CB_(2))/(T_(2)).......(ii)`
Dividin equation (i) by (ii) we get
`(M_(1))/(M_(2))=(B_(1))/(B_(2)).(T_(2))/(T_(1))Rightarrow (M_(1))/(M_(2))=(0.6)/(0.2)xx(16)/(4)`
`(8)/(M_(2))=3xx4`
`M_(2)=(8)/(12)=(2)/(3)Am^(-1)`