A paramagnetic sample shows a net magnetization of 8 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 a temperature

Question

Quantrex Academy · Accepted Answer

Correct answer: A. (2)/(3)

According to Curie's law, the magnetization

M

of a paramagnetic material is directly proportional to the external magnetic field

B

and inversely proportional to the absolute temperature

T

.

M \propto \dfrac{B}{T}

\dfrac{M_2}{M_1} = \dfrac{B_2}{B_1} \times \dfrac{T_1}{T_2}

Substituting the given values:

M_1 = 8 \text{ A/m}, B_1 = 0.6 \text{ T}, T_1 = 4 \text{ K}

B_2 = 0.2 \text{ T}, T_2 = 16 \text{ K}

\dfrac{M_2}{8} = \left(\dfrac{0.2}{0.6}\right) \times\left(\dfrac{4}{16}\right)<br><br>\dfrac{M_2}{8} = \dfrac{1}{3} \times \dfrac{1}{4} = \dfrac{1}{12}<br><br>

M_2 =

\dfrac{8}{12} = \dfrac{2}{3} \text{ A/m}

Answer:

\dfrac{2}{3}

A paramagnetic sample shows a net magnetization of 8 A/m when...

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