A paramagnetic sample shows a net magnetisation of `0.8A-m^(-1)` when plced in an external mgnetic field of 0.8T at a temperature of 5K. Whent the same sample is placed in an external magnetic field of 0.4T at temperature of 20K, the magnetisation will be

Options

A. `0.8Am^(-1)`
B. `0.8Am^(-2)`
C. `0.1Am^(-1)`
D. `0.1Am^(-2)`

Answer

C

Explanation

For paramagnetic sample (Curie's law)`I alpha B//T`
Where, `I_(1)=0.8A//m and B_(1)=0.8T`
and `T_(1)=5K Rightarrow B_(2)=0.4T`
`" " T_(2)=20K Rightarrow I_(2)=?`
`" " (I_(1))/(I_(2))=(B_(2)//T_(1))/(B_(2)//T_(2)) Rightarrow I_(1)/(I_(2))=(B_(1)xxT_(2))/(B_(2)xxT_(1))`
`" " (0.89)/(I_(2))=(0.8xx20)/(0.4xx5) Rightarrow I_(2)=(0.4xx5)/(2)=0.1Am^(-1)`