UNIT 4
Magnetic Properties of Materials
Chapter 17
Magnet
A substance which has the property to attract magnetic substances like iron, etc. is called magnet.
Properties of Magnet
- Attractive property: It can attract small pieces of magnetic substance like nickel, iron, cobalt, etc.
- Pair of poles: Every magnet has two poles where most of its strength is concentrated.
- Directive property: When a magnet is suspended with the help of thread, it comes to rest along the north-south direction.
- Force between poles: Unlike poles attract each other and like poles repel each other.
Some Terms in Magnetism
1. Axis of Magnet
The line joining two poles of a bar magnet is called axis of magnet.
2. Equatorial Line
The line perpendicular to the axis line and passing through the midpoint of two poles is called equatorial line.
3. Real Length / Geometrical Length
The total length of a magnet between two ends is called real length.
4. Equivalent Length / Effective Length
The distance between two poles of a magnet is called effective length. The real length is always greater than effective length.
Effective length = 0.84 × Real length
5. Magnetic Dipole
The equal and opposite poles separated by certain distance is called magnetic dipole.
6. Magnetic Moment (M)
The magnetic dipole moment of a magnet is the product of strength of one pole and distance between the poles.
M = m × effective length
SI unit: ampere metre square (A m²).
7. Geographical Meridian
The plane passing through geographical axis of the earth is called geographical meridian.
8. Magnetic Meridian
The imaginary vertical plane passing through axis of bar magnet is called magnetic meridian.
Elements of Earth’s Magnetism
1. Declination
The angle between magnetic meridian and geographical meridian is called declination.
2. Dip or Inclination
The angle made by the total magnetic field with the horizontal direction at a place is known as angle of dip. In other words, it is the angle between direction of earth’s magnetic field and horizontal component of earth’s magnetic field in the magnetic meridian.
The angle of dip can be measured by using dip circle. Its maximum value is 90° at pole and its value is 0° at the equator of earth.
3. Horizontal Component of Earth’s Magnetic Field
Horizontal component of Earth’s magnetic field is defined as the component of the total intensity of Earth’s magnetic field in the horizontal direction in magnetic meridian.
Relation Between Angle of Dip and Horizontal Component of Earth’s Magnetic Field
Let H and V be the horizontal and vertical components of Earth’s magnetic field and B be the resultant magnetic field.
H = B cosδ — (i)
V = B sinδ — (ii)
Dividing equation (ii) by equation (i):
V/H = tanδ
tanδ = V/H
True and Apparent Dip
The angle of dip measured by bringing the dip circle in the magnetic meridian is called true dip.
The angle of dip measured without bringing the dip circle in the magnetic meridian is called apparent dip.
For two apparent dips δ₁ and δ₂ measured in two mutually perpendicular vertical planes:
cot²δ = cot²δ₁ + cot²δ₂
where δ is the true dip.
Magnetic Field (Magnetic Field Intensity)
When a piece of iron is placed in a region near a permanent magnet, it is found to be magnetised. The degree to which a permanent magnet magnetises another material is called magnetising field. It is denoted by H.
In any medium:
B = μH
In free space:
B = μ₀H
where μ is permeability of medium and μ₀ is permeability of free space.
Intensity of Magnetisation
It is defined as the magnetic moment developed in a magnetic substance per unit volume.
I = M/V
If M = m × effective length and volume = A × effective length:
I = [m × effective length]/[A × effective length]
I = m/A
Hence, intensity of magnetisation is also the ratio of pole strength to area of magnetic substance.
Magnetic Permeability
Magnetic permeability of a material is defined as the degree to which magnetic field can penetrate the medium. It is also defined as the ratio of magnetic field to the magnetising field.
μ = B/H
Relative Permeability
It is the ratio of permeability of any medium to the permeability of free space.
μᵣ = μ/μ₀
Magnetic Susceptibility
The property which determines how easily a magnetic specimen can be magnetised is called magnetic susceptibility.
In other words, the ratio of intensity of magnetisation to the intensity of magnetising field is called magnetic susceptibility.
χ = I/H
Relation Between Relative Permeability and Magnetic Susceptibility
The magnetic induction developed in the specimen is due to two factors:
- due to magnetising field H
- due to intensity of magnetisation I
Total magnetic induction:
B = μ₀H + μ₀I
B = μ₀(H + I)
Also:
B = μH
Therefore:
μH = μ₀(H + I)
μ/μ₀ = (H + I)/H
μᵣ = 1 + I/H
Since χ = I/H:
μᵣ = 1 + χ
Magnetic Substances
The substances which are affected by a magnetic field are called magnetic substances.
Depending upon their magnetic behaviour, magnetic substances can be divided into three classes:
Ferromagnetic
Strongly attracted
χ: large positive
μᵣ: much greater than 1
Paramagnetic
Weakly attracted
χ: small positive
μᵣ: slightly greater than 1
Diamagnetic
Weakly repelled
χ: small negative
μᵣ: slightly less than 1
Ferromagnetic Substances
The substances which are strongly attracted towards the magnet are called ferromagnetic substances.
Examples: iron, cobalt, gadolinium and their alloys, etc.
Properties
- These substances are strongly attracted by a magnet.
- When a ferromagnetic material is placed inside a magnetic field, it gets magnetised strongly in the direction of the magnetic field.
- In a non-uniform magnetic field, a ferromagnetic substance moves from weaker part of magnetic field to the stronger part.
- The susceptibility of a ferromagnetic substance has a large positive value.
- The magnetisation takes place strongly in the direction of field even in the presence of small magnetic field.
Paramagnetic Substances
The substances which are weakly attracted towards the magnet are called paramagnetic substances.
Examples: aluminium, chromium, manganese, alkali and alkaline earth metals, etc.
Properties
- These substances are feebly attracted by a magnet.
- When a paramagnetic substance is placed inside a magnetic field, it gets feebly magnetised in the direction of magnetic field.
- In a non-uniform magnetic field, a paramagnetic substance moves from weaker to the stronger part.
- When a rod of paramagnetic substance is freely suspended in a magnetic field, it rotates until it lies along the field.
- The susceptibility has small positive value.
- The susceptibility is inversely proportional to temperature. If temperature starts to increase, a paramagnetic substance begins to lose its behaviour.
Diamagnetic Substances
The substances which are repelled by the magnets are called diamagnetic substances.
Examples: antimony, copper, water, alcohol, argon, gold, tin, mercury, etc.
Properties
- These substances are feebly repelled by magnets.
- When a diamagnetic substance is placed in a magnetic field, it gets feebly magnetised in a direction opposite to that of magnetising field.
- In a non-uniform magnetic field, it tries to move from the stronger to the weaker parts of the field.
- The susceptibility of a diamagnetic substance is a small negative value.
Magnetic Hysteresis
Consider a piece of iron placed in a magnetising field H. If the value of H is increased gradually, the magnetic induction B of the iron piece also increases.
- At O, H = 0 and B = 0. When H increases, B also increases until point A is reached. Point A is called saturation point.
- If H is decreased, B decreases along a different path. When H becomes zero, B still has some value represented by point C. The value of B at this point is called retentivity or remanence.
- If H is reversed in the negative direction, B decreases to zero at point D. The value of reverse magnetising field required to make B zero is called coercivity.
- If H is further increased in reverse direction, B increases in the opposite direction until the specimen reaches negative saturation.
- When H is brought back to zero and then increased in the positive direction, the loop is completed.
The complete closed curve obtained during a cycle of magnetisation is called hysteresis loop, and the whole process is called hysteresis.
Importance of Hysteresis
- The area of hysteresis curve gives the energy lost in taking a ferromagnetic substance through one complete cycle of magnetisation.
- The hysteresis curve gives information about magnetic properties of a magnetic material such as permeability, susceptibility, retentivity and coercivity.
- The choice of magnetic materials for different uses such as permanent magnet, electric magnet and transformer core can be decided from the hysteresis curve.
Solved Numerical
Q.1 – True Dip from Two Apparent Dips
The needle of a dip circle shows an apparent dip of 45° in a particular position and 53° when the circle is rotated through 90°. Find the true dip.
Apparent dip in one position, δ₁ = 45°
Apparent dip after rotating through 90°, δ₂ = 53°
The true dip angle is given by:
cot²δ = cot²δ₁ + cot²δ₂
1/tan²δ = 1/tan²45° + 1/tan²53°
1/tan²δ = 1 + 0.5678
1/tan²δ = 1.5678
tanδ ≈ 0.7987
δ ≈ 38.7°
Discussion
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