Diamagetic materials

Paramagnetic materials

Ferromagnetic materials

No internsic magnetic moment.

Dipole induced by the external magnetic field.

According to lenz's law the induced magnetic moments are dielectric opposite

to the external magnetic field.

Will be pushed from region of high magnetic field to smallar magnetic field in an homogeneous field.

Independent of Temperature

Present in all materials

Magnetization disappears when in external field to moments.

$\overrightarrow{M} = \chi_{m}\overrightarrow{H}$

$\overrightarrow{B} = \mu\overrightarrow{H} = \mu_{o}(1+\chi_{m})\overrightarrow{H}$

$\left|\chi_m\right| \ll 1$

$\chi_m < 0$

Atoms have a parmanent magnetic moments.

Atoms with odd number of electrons have a net magnetic moment.

In bulk matter, the individual dipoles are aligned randomly and hence we magnetization is zero.

On applying an external magnetic field, that is a torque on the magnetic moment which leads to partial aligment of the moment.

The material gets magnetized.

Direction of magnetization is along the direction of the external field.

Medium gets attracted towards stronger fields in an in homogeneous field.

Magnetization depends on temperature, decreases with increasing T

Pierre Curie (1859-1906)

$x_m = c \frac {\mu_0}{T}$ : C: Curie constant

$\overrightarrow{M} = \chi_{m}\overrightarrow{H}$

$\left(x_{-1} \mid \ll 1\right)$

$x_m>0$

${\vec{B}}=\mu {\vec{H}}=\mu_0\left(1+x_m\right) \vec{H}$

$\mu \geqslant \mu_0$

Atoms have an interesic magnetic dipole moments, primarly due to electron spin.

Intersection between adjacent dipoles is very strong. (each angle interaction)

Minimum energy when magnetising momemts are parallel to each other.

Materials sub divides into regions called Domains, each spontenously magnetized to a high degree

Domain volume $\sim 10^{-18}$ to $10^{-12} m^2$

Large pieces of ferromagnetic material have many domains, smaller pieces can be single domain.

Only Ferromagnetic elements are Iron, Cobalt, Nickel, Gadolinium (Gd), and Dysprosium (Dy).

Explanation of this behavior requires quantum mechanics.

Curie temperature $T_c$

$T>T_C \text { : Paramagnetic }$

IRON: $T_C \sim 1043 \mathrm{K}$

COBALT: $T_E \sim 1480 \mathrm{K}$

Hysteresis loop: $\oint \vec{H} . \overrightarrow{d l} = I_{f_{enc}}$

Toroid of radius R of ferromagnetic material

$H 2 \pi R=N_t I$

$H=\frac{N_t}{2 \pi R} I$

Magnetic field magnetizes the piece of ferromagnetic material, it produces its own magnetic field.

B is linearly related to H, they are called linear media.

Value of $\vec{B}$ when $\vec{H}$ is reduces to zero.

B field and H field are not in phase.

Coercive Field: Value of reverse fields $\vec{H}$ requires to drive $\vec{B}$ is zero.

$\mathrm{H}_{\mathrm{c}}$

It is a characteristic of ferromagnetic materials.

B field lacks the H field.

As H field increases, the B ield increased, it got saturated, then as you start to decrease the H field, the B field decreases.

Radius = 5 cm

$N_t=100$

$H=\frac{N_t I}{2 \pi R}$

$I=0.3 A ;$

$H=\frac{100 \times 0.3}{2 \pi \times 5 \times 15^2} \simeq 100 \mathrm{A} / \mathrm{m}$

For axis coil

$B =\mu_0 H=4 \pi \times 10^{-7} \times 100 \ =4 \pi \times 10^5 T$

$H =100 \mathrm{A} / \mathrm{N}$

$\mu^{\prime} =10,000$

$B =\mu H=\mu_0 \mu, \mathrm{H} = 4 \pi \times 10^{-7} \times 10^4 \times 100 = 1.2 \mathrm{~T}$

For producing same B with axis coil

$H=\frac{B}{\mu_0}=\frac{1.2}{4 \pi \times 10^{-7}}=\frac{N_0 I}{2 \pi R}$

H axis Ferromagnetic material

The soft ferromagnetic materials are used in things like transformers or loudspeakers

Three types of primary types of materials, diamagnetic, paramagnetic, and ferromagnetic.

Ferromagnetic materials are very strong magnetic properties.

Diamagnetic have negative susceptibility.

Paramagnetic have positive susceptibility.

Our earth is associated with the magnetic field.

The center of the earth is the solid iron core.

Convection current leads to movement of ions and generate currents and these currents lead to the generation of magnetic field.

The current theory called the dynamo effect.

Earth is spinning around an axis which is inclined to the vertical.

Axis of rotation is inclined to about 23.5 degrees with respect to the perpendicular plane.

The magnetic axis is slightly displaced with respect to the geographic axis by about 11.5 degrees.

Angle between the horizontal line and the geographic north is called the declination.

The angle between the magnetic vector and the horizontal plane is called dip.

New Delhi declination is about $\sim$ $1^0 7'$.

Incination $\sim$ $44^0 34'$ (EAST).