Solid State Physics-II

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Chapter#4: Magnetism in Solids

Team Quanta gladly presents all possible short questions of BS Physics book Solid State Physics – II’s Chapter#4: Magnetism in Solids.

Q.4.1:- State Langevin’s formula for susceptibility of diamagnetic material.

    \[\chi_{dia}=\frac{M}{H}\]

∵M=N_{\mu m}

    \[\chi_{dia}=\frac{{N\mu}_m}{H}\]

∵\mu_m=-\frac{{Ze}^2\mu^oH}{6m}

    \[\chi_{dia}=\frac{N\left [- \frac{Ze^2\mu_oH}{6m} \right ]}{H}\]

    \[\chi_{dia}=-\frac{NZe^2 \mu_o H}{6mH}\]

    \[\chi_{dia}=-\frac{NZe^2 \mu_o H}{6m}\]

This is classical langevin’s formula for susceptibility of diamagnetic material and show that the diamagnetic susceptibility is independent of temperature.

Q.4.2:- How anti-ferromagnetic material becomes paramagnetic?

The antiferromagnetic material the adjacent moments are opposite to each other. When magnetic field is applied the magnetic moment tends to align themselves in the same direction. Then the antiferromagnetic material becomes paramagnetic.

Q.4.3:- Define Curie constant and Curie temperature.

Curie constant:

The paramagnetic susceptibility is given by;

    \[\chi_{para}=\frac{C}{T}\]

The equation is called curie equation and the constant C=\frac{N\mu^2 \mu_o}{K}  is called curie constant.

Curie temperature:

 The spontaneous magnetization can occur below a certain temperature is called Curie temperature.

    \[\chi=\frac{M}{H}\]

Q.4.4:- Define magnetic susceptibility and permeability.

Magnetic susceptibility:-

The ratio of magnetization of the induced magnetizing field is called magnetic susceptibility.

Permeability:-Permeability is a measure of magnetization that a material obtain in response to an applied magnetic field.

    \[\mu_r= \frac{\mu }{\mu _o}\]

Q.4.5:- Distinguish between paramagnetic, diamagnetic and ferromagnetic materials.

Paramagnetic material:-

The paramagnetic material have small, positive and temperature dependent susceptibility. The paramagnetic material, the magnetic moment are aligned in the direction of magnetic field.

Diamagnetic material:-

In the diamagnetic material, the diamagnetic is opposite to the direction of field of induced. So that is negative. The value of magnetic induced is smaller in the diamagnetic.

Ferromagnetic material:-

Ferromagnetic material has spontaneous magnetic moments, magnetic moments in the same direction magnetic moment are present even zero applied magnetic field.

Q.4.6:-What are domains?

“ferromagnetism occurs when paramagnetic ions in a solid ‘lock’ to gather in a small regions in which all magnetic moments are along the same direction. Such a region called domains”

Each domain contain a volume {10}^{-12} \ to \ {10}^{-8}m^{3\ } \ and \ {10}^{17} \ to \ {10}^{21} \ atoms.

 Q.4.7:- Define curie Weiss law and write its mathematical.

Ferromagnetism arises when the magnetic moments of adjacent atoms are arranged in a regular order i.e. all pointing in the same direction. This ferromagnetic substance thus possess a magnetic moment even in the absence of the applied magnetic field. This magnetization is called spontaneous magnetization.

Mathematical form:

    \[H_m\propto I\]

    \[H_m=\ \leftthreetimes I\]

Where ⋋ is Weiss constant and is independent of temperature.

Q.4.8:- Write the physical significance of the langevin’s formula of susceptibility of the diamagnetic material; \chi=-\frac{\mu _o NZe^2}{6m}

Physical significance: The diamagnetic susceptibility is given by;

 \chi=-\frac{\mu _o NZe^2}{6m}. Thus show that the diamagnetic susceptibility is independent of temperature. The negative sign signifies that the induced magnetic moment points in a direction opposite to the applied field.

Q.4.9:- Define Bohr Magneton and write mathematical equation for Land’s factor g.

Bohr magneton: The ratio between charge and mass is called Bohr magneton.

    \[\mu_B=\frac{\hbar e}{2m}\]

The numerical value of Bohr magneton is, \mu_B=9.274\ast{10}^{-24}\frac{J}{T}.

Land’s factor: The magnetic moment in free space is given as;

    \[\mu=\ -g\mu_BJ\]

‘g’ is called Land’s factor. For free electron g is given by;

    \[g=1+\frac{J\left(J+1\right)L\left(L+1\right)S(S+1)}{2J(J+1)}\]

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