## Sunday, March 23, 2008

### Concept Review Ch.37 Magnetic Properties of Matter

Revision Points
(Revision points help you during the revision process. After you have read the text once or twice, and understood its contents well, revision points help you to study the material quickly and also help you to recollect more details described in the text book)

A current loop has magnetic dipole movement. Hence each electron in an atom has a magnetic moment due to its orbital motion. Besides this, each electron at rest also has a permanent angular momentum, which is called spin angular momentum (The concept was explained in chemistry atomic structure chapter as well as in the Bohr model chapter of physics). This magnetic moment has a fixed magnitude μs = 9.285*10^-24 J/T.

The resultant magnetic moment of an atom is the vector sum of magnetic moment due orbital movement and spin angular momentum.

The magnetic moments of the electrons of an atom have tendency to cancel in pairs. For example, the magnetic moments of a helium atom cancel each other.

In some atoms such a cancellation is not there and the magnetic moment of an atom is not zero. Such atoms can be represented by a magnetic dipole.

In general magnetic moments of atoms are randomly oriented and there is no net magnetic moment in any volume of material that contains several thousand atoms. However, when material is kept in an external magnetic field, torques act on the atomic dipoles and these torques align them parallel to the field. The degree of alignment increases if the strength of the applied field is increased and also if the temperature is decreased. With sufficiently strong field, the alignment is near perfect and we say the material is magnetically saturated.

When the atomic dipoles are aligned, partially or fully, there is a net magnetic moment in the direction of the field in any small volume of the material.

Magnetization vector I is defined as the magnetic moment per unit volume. It is also called the intensity of magnetization of simply magnetization.

There fore I = M/V

Where M = magnetic moment in units ampere-metre²
V = volume
Units of I are ampere/metre

Bar magnet case:

In case of a bar magnet with pole strength of m, length 2l and area of cross section A, magnetic moment is 2ml.

Hence I = M/V = 2ml/A(2l) = m/A

So we see that in the case of bar magnet, intensity of magnetization turns out to be pole strength per unit face area.

Paramagnetism

The tendency to increase the magnetic field due to magnetization of material is called paramagnetism and materials which exhibit this property are called paramagnetic materials.

Ferromagnetic materials

In some materials, the permanent atomic magnetic moments have strong tendency to align themselves without any external field. Because of this tendency, even if a small magnetic field is applied, it gives rise to large magnetization. These materials are called ferromagnetic materials.

Diamagnetism

In many materials, individual atoms do not have net magnetic dipole moment. When such materials are placed in a magnetic field, dipole moments are induced in the atoms by the applied field. The field so induced opposes the original field. Hence the resultant field will be smaller. This phenomenon is called diamagnetism.

All materials are diamagnetic. But in some materials which are paramagnetic and ferromagnetic, diamagnetism will not be shown.

Magnetic Intensity

When a magnetic field is applied to a material, the material gets magnetized. The actual magnetic field inside the material is the sum of the applied magnetic field and the magnetic field due to magnetization of the material.

If B is the resulting magnetic field it will be equal to μ0(H + I)

Where H is magnetizing field intensity, I = Intensity of magnetization of the material.

Units of H are units of I, that ampere/metre

If no material is there B = μ0H

Magnetic susceptibility

For paramagnetic and diamagnetic substances, the intensity of magnetization of a material is directly proportional to the magnetic intensity.

I = χH

The proportionality constant χ is called the susceptibility of the material. Materials with positive χ values paramagnetic and materials with negative χ value are diamagnetic materials.

Permeability

B = μ0(H + I) = μ0(H + χH)
= μ0(1 + χ)H

We can write it as B = μH

μ is called permeability of the material. The permeability of vacuum is μ0 as χ = 0.

μr = μ/μ0 = 1 + χ is called the relative permeability,

Take a solenoid. The magnetic field inside is B0.
When a material is inserted in the solenoid, the magnetic field becomes B and B/ B0 and this will be μr of the material.

Curie’s law

As the temperature is increased, the randomization of individual atomic magnetic moments increases and hence magnetization of a given material for a given applied magnetic intensity decreases. This means that χ decreases as T increases.

Curie’ law states that in the region away from saturation, the susceptibility (χ) of a paramagnetic substance is inversely proportional to the absolute temperature.

Χ = c/T

Where c is a constant called Curie constant.

Curie point: Ferromagnetic material becomes paramagnetic at a certain temperature. This temperature is called Curie point or Curie temperature (Tc).

The susceptibility of such materials after the Curie point follows the Curie’s law with the formula χ = c’/(T - Tc). c' is the constant.

Properties of Dia-, Para-, and Ferromagnetic substances

1. The lines of magnetic field become denser in a paramagnetic or ferromagnetic materials and less dense in diamagnetic materials.

2. The magnetic susceptibility is a small but positive quantity for paramagnetic substances. It is of the order of several thousand for ferromagnetic materials. For diamagnetic material it is small negative quantity.

3. Ferromagnetism is normally found in solids only.

4. A paramagnetic substance is weakly attracted by a magnet. A ferromagnetic substance is strongly attracted by the magnet. Diamagnetic substance is weakly repelled by the magnet.

Hysteresis

A ferromagnetic material when it is magnetized once will not come back to zero when the current becomes zero in the current carrying coil. To reduce it to zero current in the opposite direction must be passed.

As H is increased and then decreased to its original value, the magnetization inside a ferromagnetic material does not return to its original value. This fact is called hysteresis.

Soft Iron and Steel

Soft iron is easily magnetized by a magnetizing field but only a small magnetization is retained when the field is removed. The loss of energy, as the material goes through periodic variations in magnetizing fields is small. Soft iron is suitable for making electromagnets and cores inside current carrying coils to increase the magnetic field.

Steel is more suitable for making permanent magnets. Large field is required to magnetize but the field is retained to a large extent and it is not easily destroyed by stray reverse fields. The coercive force is large.