Magnetic Properties of Materials

Answers & Solutions

Work the questions above first, then check yourself here. Each answer is set out the way it should be written in the paper.

1. 1.↑ back to the question

   Domain theory: i. In ferromagnetic materials, interaction called exchange coupling or exchange interaction between neighbouring magnetic dipole moments is strong. ii. Due to this interaction, small regions called domain are formed in which all the atoms have their magnetic moments aligned in the same direction. The common direction of magnetic moment is called the domain axis. Domain size can be a fraction of a millimetre ($10^{-6}-10^{-4}$ m) and contains about $10^{10}-10^{17}$ atoms. iii. The boundary between adjacent domains with a different orientation of magnetic moment is called a domain wall. iv. In unmagnetized state, even though the magnetic moment of individual domains are non-zero, the domain axes of different domains being oriented randomly, the net magnetic moment of the whole material is zero. v. When an external magnetic field is applied, flipping or domain rotation occurs. In this process, domains try to align themselves along the direction of the applied magnetic field. The number of domains aligning in that direction increases as magnetic field is increased. vi. When sufficiently high magnetic field is applied, all the domains coalesce together to form a giant domain as shown in figure. vii. When the strong external magnetic field is completely removed, the domain boundaries are not set back to original position resulting in the net magnetic moment remaining non-zero and the ferromagnetic material is said to retain magnetization. Such materials are used in preparing permanent magnets. viii. In non-uniform magnetic field, ferromagnetic material tends to move from weaker part to stronger part of the field.

2. 2.↑ back to the question

   No.	Diamagnetic Substance	Ferromagnetic Substance
   i.	They are weakly repelled by magnet.	They are strongly attracted by magnet.
   ii.	If a thin rod of diamagnetic substance is freely suspended in uniform magnetic field, it comes to rest slowly with its length perpendicular to the direction of magnetic field.	If a thin rod of ferromagnetic substance is freely suspended in a uniform magnetic field, it comes quickly to rest with its length parallel to the direction of the field.
   iii.	When placed in non uniform magnetic field, they show a moderate tendency to move from the stronger to the weaker part of the field.	When placed in non uniform magnetic field, they show a strong tendency to move from the weaker to the stronger part of the field.
   iv.	In the absence of external magnetic field, the resultant magnetic moment of each atom is zero.	The resultant magnetic moment of each atom of a ferromagnetic substance is much greater than zero.
   v.	There is no effect of temperature on diamagnetic substance.	There is effect of temperature on ferromagnetic substance.
   vi.	They cannot be permanently magnetised.	They can be permanently magnetised.

   [Any two points]

3. 3.↑ back to the question

   No.	Paramagnetic substance	Ferromagnetic substance
   i.	It is weakly attracted by a magnet.	It is strongly attracted by a magnet.
   ii.	When kept in a non-uniform magnetic field, it shows moderate tendency to move from weaker to the stronger part of the field.	When kept in a non-uniform magnetic field, it shows strong tendency to move from weaker to the stronger part of the field.
   iii.	When kept in an external magnetic field it becomes weakly magnetised, and the direction of magnetic moment acquired will be same as that of the field.	When kept in an external magnetic field it becomes strongly magnetised, and the direction of magnetic moment acquired will be same as that of the field.
   iv.	When the external magnetic field is removed, the paramagnetic substance loses its magnetism.	When the external magnetic field is removed, the ferromagnetic substance retains magnetism permanently.
   v.	They cannot be converted into ferromagnetic substances.	When heated above curie temperature, they become paramagnetic substances.
   vi.	Every atom has some magnetic dipole moment but resultant dipole moment is zero.	The resultant magnetic dipole moment is greater.
   vii.	They can be temporarily magnetised in external magnetic field.	They can be permanently magnetised.

4. 4.↑ back to the question

   The question is a real board question. Its answer and working are ours — this paper was published without an official answer key.

   What the diagrams show

   • i. A paramagnetic substance is made of atoms (or molecules) that have unpaired electrons, so every atom already possesses a permanent magnetic dipole moment. Each such moment is drawn as a small arrow.
   • ii. When the external magnetic field is absent, thermal agitation keeps these atomic dipole moments randomly oriented. Their vector sum is zero, so the resultant magnetization of the specimen is zero and it shows no magnetism.
   • iii. When a strong external magnetic field is applied (especially at low temperature, where thermal agitation is reduced), most of the dipole moments turn and align themselves along the direction of the applied field, because that is the orientation of minimum magnetic potential energy, $U_m = -mB$.
   • iv. The specimen is then weakly magnetised in the direction of the applied field, the lines of force inside it come closer together, and its magnetization $M$ is large but still small compared with that of a ferromagnetic material.
   • v. The two diagrams are shown side by side: randomly oriented dipole arrows with no external field, and dipole arrows lined up along the field when a strong external field is applied.

   Result

   $$\boxed{\ \text{No field: } \vec{M} = 0\ (\text{random dipoles});\qquad \text{Strong field: } \vec{M} = \chi\vec{H}\ \text{along}\ \vec{B}\ (\text{aligned dipoles})\ }$$

   • On removing the field the dipoles become random again, so the magnetisation of a paramagnetic substance is only temporary.

   
5. 5.↑ back to the question

   No.	Diamagnetic substance	Paramagnetic substance
   i.	In an external magnetic field, a substance gets weakly magnetised in the direction opposite to that of the field.	In an external magnetic field, a paramagnetic substance gets weakly magnetised in the same direction as that of the field.
   ii.	When placed in a non-uniform magnetic field, it tends to move from the stronger to the weaker part of the field.	When placed in a non-uniform magnetic field, it tends to move from the weaker to the stronger part of the field.
   iii.	It is weakly repelled by a magnet.	It is weakly attracted by a magnet.
   iv.	Magnetic moment of every atom of a diamagnetic substance is zero.	Every atom of a paramagnetic substance is a magnetic dipole having a certain resultant magnetic moment.
   v.	When a rod of diamagnetic substance is suspended in a uniform magnetic field, it comes to rest with its length perpendicular to the direction of the field.	When a rod of paramagnetic substance is suspended in a uniform magnetic field, it comes to rest with its length parallel to the direction of the field.
   vi.	There is no effect of temperature on diamagnetic substance.	There is effect of temperature on paramagnetic substance.

6. 6.↑ back to the question

   i. The temperature at which a ferromagnetic material transforms into a paramagnetic substance is called Curie temperature ($T_c$) of that material. ii. An increase in the temperature of a ferromagnetic material weakens the exchange coupling between neighbouring moments which results in the domain structure getting distorted. iii. Above Curie temperature the domain structure of a ferromagnetic material collapses totally and the material behaves like paramagnetic material.

7. 7.↑ back to the question

   When heated above Curie temperature, ferromagnetic substances become paramagnetic substances.

8. 8.↑ back to the question

   When the rod of diamagnetic material is placed in a non-uniform magnetic field, it tends to move from stronger part to the weaker part of the magnetic field.

9. 9.↑ back to the question

   Given: $\chi_1=2.4\times10^{-5}$, $T_1=300$ K, $\chi_2=3.6\times10^{-5}$ To find: Required temperature ($T_2$) Formula: χT = constant Calculation: From formula, $\chi_1T_1=\chi_2T_2$ $$\therefore T_2=\dfrac{\chi_1T_1}{\chi_2}=\dfrac{2.4\times10^{-5}\times300}{3.6\times10^{-5}}=\dfrac{2\times300}{3}$$ $\therefore T_2=200$ K Ans: The temperature at which the susceptibility will increase to $3.6\times10^{-5}$ is 200 K.

10. 10.↑ back to the question

    Given: $T_1=200$ K, $\chi_1=1.8\times10^{-5}$, $\chi_1-\chi_2=6\times10^{-6}$ $\Rightarrow \chi_2=1.8\times10^{-5}-0.6\times10^{-5}=1.2\times10^{-5}$ To find: Required temperature ($T_2$) Formula: χT = constant Calculation: From formula, $\chi_1T_1=\chi_2T_2$ $$\therefore T_2=\dfrac{\chi_1T_1}{\chi_2}=\dfrac{1.8\times10^{-5}\times200}{1.2\times10^{-5}}=300\text{ K}$$ Ans: The required temperature is 300 K.

11. 11.↑ back to the question

    Given: $\chi_1=1.2\times10^{-5}$, $T_1=300$ K, $\chi_2=1.8\times10^{-5}$ To find: Required temperature ($T_2$) Formula: χT = constant Calculation: From formula, $\chi_1T_1=\chi_2T_2$ $$\therefore T_2=\dfrac{\chi_1T_1}{\chi_2}=\dfrac{1.2\times10^{-5}\times300}{1.8\times10^{-5}}$$ $\therefore T_2=200$ K Ans: The required temperature is 200 K.

12. 12.↑ back to the question

    Given: $\chi_1=1.2\times10^{-5}$, $T_1=300$ K, $T_2=200$ K To find: Susceptibility at temperature $T_2$ ($\chi_2$) Formula: χT = constant Calculation: From formula, $\chi_1T_1=\chi_2T_2$ $$\therefore \chi_2=\dfrac{\chi_1T_1}{T_2}=\dfrac{1.2\times10^{-5}\times300}{200}$$ $\therefore \chi_2=1.8\times10^{-5}$ Ans: The susceptibility at 200 K is $1.8\times10^{-5}$.

13. 13.↑ back to the question

    Given: $\chi_1=1.2\times10^{-5}$, $T_1=300$ K, $\chi_1-\chi_2=0.4\times10^{-5}$ $\therefore \chi_2=(1.2-0.4)\times10^{-5}=0.8\times10^{-5}$ To find: Temperature ($T_2$) Formula: χT = constant Calculation: From formula, $\chi_1T_1=\chi_2T_2$ $$\therefore T_2=\dfrac{\chi_1T_1}{\chi_2}=\dfrac{1.2\times10^{-5}\times300}{0.8\times10^{-5}}$$ $\therefore T_2=450$ K Ans: Required temperature is 450 K.