Behaviour of substances in magnetic field - class-XII

Iron, cobalt and nickel are the examples of ferromagnetic material.

Above Curie temperature, ferromagnetic material become paramagnetic.

Electrons is an atom orbiting around nucleus possess orbital angular momentum. These orbiting electrons are equivalent to current-carrying loop and thus possess orbital magnetic moment. Diamagnetic substances are the ones in which resultant magnetic moment in an atom is zero. When magnetic field is applied, those electrons having orbital magnetic moment in the same direction slow down and those in the opposite direction speed up. Thus, the substance develops a net magnetic moment in direction opposite to that of the applied field.

At enough high temperature, a ferromagnet become a paramagnet. The domain structure disintegrates with temperature.

The susceptibility of a paramagnetic substance is inversely proportional to absolute temperature.
$X \propto \frac{1}{T}$
Hence $XT = constant$
Also for paramagnetic substances the susceptibility is positive and very small.

Here, $\chi =-1$
then $\mu _r=1+\chi \Rightarrow \mu _r=1+(-1)=I-1=0$
Since, magnetic susceptibility of given material is less than one. Hence, the given magnetic material is a diamagnetic material.

The volume of the cubic domain
$V=(2\mu m)^3=(2\times 10^{-6}m)^3$
$=8\times 10^{-18}m^3=8\times 10^{-12}cm^3$
and mass $=$volume $\times$ density
$=8\times 10^{-12}cm^3\times 7.9g cm^{-3}$
$=63.2\times 10^{-12}$g
Now the Avagadro number $(6.023\times 10^{23})$ of iron atoms have a mass of $55$g. Hence the number of atoms in the domain are.
$N=\dfrac{63.2\times 10^{-12}\times 6.023\times 10^{23}}{55}=6.92\times 10^{11}$ atoms.

Diamagnetic substances induce magnetic field in the direction opposite to an external applied magnetic field and thus are repelled by external applied magnetic field.

diamagnetic
$-1 \leq x < 0$
$\chi =susceptibility$

Paramagnetic material $0< \chi < \varepsilon $
$\varepsilon $ it small, positive and less than one.
$\chi $ is suscepticity

Diamagnetic          Paramagnetic             ferromagnetic
-1 $\leq$ $\chi$ < 0            0 < $\chi$ < $\varepsilon$                 $\chi$ >>1
$\chi $$=$magnetic susceptibility

-1, Because superconductor are perfect diamagnetic substances.

For ferromagnetic substances, $\chi _m$ is large and positive.

A superconductor exhibits perfect diamagnetism.

Magnetic susceptibility is a dimensionless proportionality constant that indicates the degree of magnetisation of a material in response to an applied magnetic field.

Diamagnetic substances are those which are freebly repelled by the magnetic field.
$\therefore$ Copper, Hydrogen, Silver are diamagnetic as their atoms have net magnetic dipole moment zero.

Diamagnetism (where orbital motion of electrons creates tiny atomic current loops, which produce magnetic fields) is a property of all materials and opposes applied magnetic fields, but is very weak.

Here when electromagnet is connected to battery, emf source the magnetic field is produced which pushes rod upwards and so gravitational potential energy is stored.

A paramagnet magnet behaves like a solenoid because both contain currents in the form of circle. The magnetic field is generated by the circular motion of the electron inside the atom.

Ferromagnetism materials exhibit a long range ordering phenomenon at the atomic level which causes the unpaired electron spins to line up parallel with each other in a region called domain. Within the domain, the magnetic field is intense, but in a bulk sample the material will usually be unmagnetised because the many domains will themselves be randomly oriented with respect to one another. Hence, domain formation is the necessary feature of ferromagnetic substance.

Ferromagnetic materials are strongly attracted to magnetic fields. When placed in a non-uniform magnetic field (like between the poles of a magnet), the liquid will be pulled toward the region of higher field strength, causing the level in that arm to rise.

The magnetic susceptibility of a diamagnetic material is negative and essentially independent of temperature T because diamagnetism arises from the orbital motion of electrons which is largely unaffected by thermal agitation.

Paramagnetic substance gets feebly magnetised in the direction of field and therefore, $I$ is very small and positive for paramagntic substances.
We know $X _m=I/H$
Therefore,$X _m$ is also very small and positive.

For diamagnetic material
$0\leq \mu _{r}< 1$
And for any material, $ \varepsilon _{r}> 1$

Magnetization is present in all materials. It is a class of physical phenomenon that is mediated by Magnetic fields.

The magnetic state of different materials depends on temperature and other variables such as pressure and applied magnetic field.

For a diamagnetic material, $\mu _r$ and $\epsilon _r$ should have following bounds $0<\mu _r <1$ and for any material $\epsilon _r >1$

Ferromagnetic substances are strongly attracted by a magnet while, paramagnetic and diamaganetic substances are weakly attracted and repelled respectively.

The Curie temperature is the temperature above which ferromagnetic materials lose their permanent magnetic field, the magnetism completely disappears. Above Curie temperature, the material behaves para-magnetically.

When a ferromagnetic material is placed in an external magnetic field, the magnetic domains that are aligned with the field grow in size at the expense of those that are not, leading to magnetization.

Magnetic susceptibility is defined as the ratio of magnetization to the magnetic field intensity. For diamagnetic materials, the induced magnetization is in the opposite direction to the applied field, resulting in negative susceptibility.

Diamagnetic           Paramagnetic             Ferromagnetic
-1 $\leq$ $\chi$ < 0                  0 < $\chi$ < $\varepsilon$                  $\chi$ >> 1
0 $\leq$ $\mu _{r}$ < 1                1 < $\mu _{r}$ < 1+ $\varepsilon$               $\mu _{r}$ >> 1
$\chi$ $=$ magnetic susceptibility
$\mu _{r}$ $=$ relative permeability.
$\varepsilon$ < 1 and small.

diamagnetic material
$-1\leq \chi < 0$
0 $\leq$ $\mu$ < 1
$\chi$ $=$ Magnetic susceptibility
$\mu$ $=$ permeability

Diamagnetic sultance
-1 $\leq$ $\chi < 0$ 
$\theta =\mu < 1$
$\chi =susceptibility$