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Question
A paramagnetic sample shows a net magnetisation of 8 Am–1 when placed in an 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 a temperature of 16 K, the magnetisation will be ______.
Options
`32/3` Am–1
`2/3` Am–1
6 Am–1
2.4 Am–1
Solution
A paramagnetic sample shows a net magnetisation of 8 Am–1 when placed in an 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 a temperature of 16 K, the magnetisation will be `underline(2/3 Am^(–1))`.
Explanation:
i.e., `I("magnetization") oo (B("magnetic field induction"))/(t("temperature in kelvin"))`
⇒ `I_2/I_1 = B_2/B_1 xx t_1/t_2`
Let us suppose, here `I_1 = 8 Am^(-1)`
`B_1 = 0.6 T, t_1 = 4 K`
`B_2 = 0.2 T, t_2 = 16 K`
`I_2` = ?
⇒ `0.2/0.6 xx 4/16 = I_2/8`
⇒ `I_2 = 8 xx 1/12 = 2/3 Am^(-1)`
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