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

Answer

D

Explanation

For paramagnetic sample ( Curie's law ) `l prop B//T ` where ,`l_(1) =0.8Am^(-1) and B_(1) =0.8 T`
`T_(1) 5K implies B_(2)=0.4T`
`T_2=20K and l_(2)=?`
`(l_(1))/(l_(2))=(B_(1)//T_(1))/(B_(2)//T_(2))implies (l_(1))/(l_(2))=(B_(1) xx T_(2))/(B_(2) xx T_(1))`
` or (0.8)/(l_(2))=(0.8 xx 20)/(0.4 xx 5) implies l_(2) =(0.4 xx 5)/(20) =0.1 Am^(-1)`