A paramagnetic sample shows a net magnetisation of <math> <mn>12</mn> <mtext> </mtext> <mi mathvariant="normal">A</mi> <mo>/</mo> <mi mathvariant="normal">m</mi> </math> when placed in an external magnetic field of <math> <mn>0.6</mn> <mtext> </mtext> <mi mathvariant="normal">T</mi> </math> at a temperature of <math> <mn>4</mn> <mtext> </mtext> <mi mathvariant="normal">K</mi> </math> . When the same sample is placed in an external magnetic field of <math> <mn>0.2</mn> <mtext> </mtext> <mi mathvariant="normal">T</mi> </math> at temperature of 16 k, the net magnetisation will be <math> <mi mathvariant="normal">A</mi> <mo>/</mo> <mi mathvariant="normal">m</mi> </math> .

M = χ m H and χ m = C T ( Curie law ) , M = C H T or M 1 M 2 = C H 1 / T 1 C H 2 / T 2 = H 1 H 2 T 2 T 1 M 2 = M 1 H 2 H 1 T 1 T 2 = 12 ( A / m ) 0.2 T 0.6 T 4 K 16 K = 1 A / m

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Physics NCERT Exemplar Solutions Class 11th Chapter Fifteen Physics Class 12th Physics Magnetism and Matter

A paramagnetic sample shows a net magnetisation of $12 A / m$ 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 temperature of 16 k, the net magnetisation will be $A / m$ .

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Raj Pandey | Contributor-Level 9

3 weeks ago

$M = χ_{m} H$ and $_{} \frac{}{}$ $χ_{m} = \frac{C}{T} ($ Curie law $)$ ,

$M = \frac{C H}{T}$ or $\frac{M_{1}}{M_{2}} = \frac{C H_{1} / T_{1}}{C H_{2} / T_{2}} = (\frac{H_{1}}{H_{2}}) (\frac{T_{2}}{T_{1}})$ $\frac{_{}}{_{}} \frac{_{}_{}}{_{}_{}} (\frac{_{}}{_{}}) (\frac{_{}}{_{}})$

$M_{2} = M_{1} (\frac{H_{2}}{H_{1}}) (\frac{T_{1}}{T_{2}}) = 12 (A / m) [\frac{0.2 T}{0.6 T}] [\frac{4 K}{16 K}]$

$= 1 A / m$

<math> <mi>M</mi> <mo>=</mo> <msub> <mrow> <mrow> <mi>χ</mi> </mrow> </mrow> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> </msub> <mi>H</mi> </math> and <math><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub><mfrac><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></mfrac></math> <math> <msub> <mrow> <mrow> <mi>χ</mi> </mrow> </mrow> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>C</mi> </mrow> </mrow> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> </mfrac> <mo>(</mo> </math> Curie law <math></math> <math> <mo>)</mo> </math> ,<math></math> <math> <mi>M</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>C</mi> <mi>H</mi> </mrow> </mrow> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> </mfrac> </math>  or <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>M</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>M</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>C</mi> <msub> <mrow> <mrow> <mi>H</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo>/</mo> <msub> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mi>C</mi> <msub> <mrow> <mrow> <mi>H</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <mo>/</mo> <msub> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>H</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>H</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </math> <math><mfrac><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow></mfrac><mfrac><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow></mfrac><mfenced separators="|"><mrow><mrow><mfrac><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow></mfrac></mrow></mrow></mfenced><mfenced separators="|"><mrow><mrow><mfrac><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow></mfrac></mrow></mrow></mfenced></math> <math> <msub> <mrow> <mrow> <mi>M</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mrow> <mi>M</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>H</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>H</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> <mo>=</mo> <mn>12</mn> <mo>(</mo> <mtext> </mtext> <mi mathvariant="normal">A</mi> <mo>/</mo> <mi mathvariant="normal">m</mi> <mo>)</mo> <mfenced open="[" close="]" separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>0.2</mn> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mn>0.6</mn> <mi>T</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> <mfenced open="[" close="]" separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>4</mn> <mtext> </mtext> <mi mathvariant="normal">K</mi> </mrow> </mrow> <mrow> <mrow> <mn>16</mn> <mtext> </mtext> <mi mathvariant="normal">K</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </math> <math> <mo>=</mo> <mn>1</mn> <mtext> </mtext> <mi mathvariant="normal">A</mi> <mo>/</mo> <mi mathvariant="normal">m</mi> </math>

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A paramagnetic sample shows a net magnetisation of $12 A / m$ 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 temperature of 16 k, the net magnetisation will be $A / m$ .

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A paramagnetic sample shows a net magnetisation of 12 A / m 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 temperature of 16 k, the net magnetisation will be A / m .

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A paramagnetic sample shows a net magnetisation of $12 A / m$ 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 temperature of 16 k, the net magnetisation will be $A / m$ .