A paramagnetic sample shows a new magnetisation of `8 "Am"^(-1)` when placed in and external magnetic field of 0.6 T at a temperature of 4 K. When the same sample is placed in an external magnetic field of 0.2 T at temperature of `16` K, the magnetisation will be

Options

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

Answer

B

Explanation

According to Curie.s law, intensity of magnetization directly proportional to the magnetic field induction and inversely proportional to its absolute temperature.
So magnetisation,
`I prop (B)/( T)`
`therefore I_(1) prop (B_1)/( T_1) and I_(2) prop (B_2)/( T_(2))`
`therefore (I_2)/( I_1) = (B_2)/( B_1) xx (T_1)/( T_2) `
`I_1= 8 "Am"^(-1) , "Taking" B_(1) = 0.6 T, T_(1) = 4K`
`B_(2) = 0.2 T , T_(2) = 16` K
`(I_2)/( 8) = ((0.2)/( 0.6)) ((4)/(16))`
`I_(2) = (8)/(12) = (2)/(3) "Am"^(-1)`