When a current-carrying solenoid is suspended by a long thread so that it can move freely in the horizontal plane, it comes to rest in the north–south direction. The end of the solenoid other than the one pointing towards the north is called the ‘south pole’.
Definitions [32]
Define Curie temperature.
The temperature above which a ferromagnetic substance becomes paramagnetic is called curie temperature.
Definition: Gyromagnetic Ratio
The ratio of the magnitude of the magnetic dipole moment to the magnitude of the angular momentum of the revolving electron is a constant, independent of the details of the orbit. This ratio is called the ‘gyromagnetic ratio’ for the electron.
Definition: North Pole
When a current-carrying solenoid is suspended by a long thread so that it can move freely in the horizontal plane, then it always rests in the north-south direction. The end of the solenoid pointing north is called the ‘north pole'.
Definition: Bohr Magneton
The minimum value of the magnetic dipole moment of an electron is called the Bohr magneton. 1 Bohr-magneton = 9.27 × 10-24 A-m².
Definition: Magnetic Lines of Force
The lines of force in a magnetic field are those imaginary lines which continuously represent the direction of the magnetic field. The tangent drawn at any point on a line of force shows the direction of magnetic field at that point.
Definition: Horizontal Component of Earth's Magnetic Field
The horizontal component is the component of the earth’s magnetic field in the horizontal direction in the magnetic meridian.
Definition: Angle of Dip or Magnetic Inclination
The angle of dip at a place is the angle between the direction of earth's magnetic field and the horizontal in the magnetic meridian at that placе.
Definition: Angle of Declination
At any place, the acute angle between the magnetic meridian and the geographical meridian is called the 'angle of declination'.
Definition: South Pole
Definition: Magnetic Equator
The plane perpendicular to the magnetic axis of the earth and passing through the points where the magnetic needle is parallel to the earth's surface intersects the earth’s spherical surface into a circle. This 'circle' is called the 'magnetic equator' of the earth.
Definition: Magnetic Axis
The line joining the magnetic north and the magnetic south poles of the earth is called the 'magnetic axis' of earth.
Definition: Geomagnetic Poles of the Earth
The two places where the needle becomes perpendicular to the Earth’s surface, that is, vertical, are called the geomagnetic poles of the Earth.
Definition: Hysteresis
The lagging of intensity of magnetisation (I) or magnetic induction (B) behind the magnetising field (H) during the process of magnetisation and demagnetisation of a ferromagnetic material is called hysteresis.
Definition: Retentivity
The residual value of magnetic induction (B) retained by a ferromagnetic material when the magnetising field (H) is reduced to zero (represented by point B/C on the hysteresis loop) is called retentivity.
Definition: Coercivity
The value of the reverse magnetising field (H₀) required to reduce the residual magnetic induction of a ferromagnetic material to zero (represented by point F on the hysteresis loop) is called coercivity.
Definition: Magnetic Susceptibility
It may be defined as the ratio of the intensity of magnetisation to the magnetic intensity of the magnetising field,
\[\chi_m=\frac{M}{H}\]
Definition: Diamagnetism
Some substances, when placed in a magnetic field, are feebly magnetised opposite to the direction of the magnetising field. When brought close to a pole of a powerful magnet, they are somewhat repelled away from the magnet. These substances are called 'diamagnetic' substances and their magnetism is called 'diamagnetism'.
Definition: Paramagnetism
Some substances when placed in a magnetic field, are feebly magnetised in the direction of the magnetising field. When brought close to a pole of a powerful magnet, they are attracted towards the magnet. These substances are called 'paramagnetic' substances and their magnetism is called 'paramagnetism'.
Definition: Ferromagnetism
Some substances, when placed in a magnetic field are strongly magnetised in the direction of the magnetising field. They are attracted fast towards a magnet when brought close to either of the poles of the magnet. These substances are called 'ferromagnetic' substances and their magnetism is called 'ferromagnetism'.
Definition: Magnetic Induction
When a piece of any substance is placed in an external magnetic field, the substance becomes magnetised. The magnetism so produced in the substance is called 'induced magnetism' and this phenomenon is called 'magnetic induction'.
Definition: Magnetic Lines of Induction
The magnetic lines of force inside the magnetised bar are called 'magnetic lines of induction'.
Definition: Magnetic Flux Density
The number of magnetic lines of induction inside a magnetised substance crossing unit area normal to their direction is called the magnitude of magnetic induction or magnetic flux density, inside the substance.
Definition: Intensity of Magnetisation
The intensity of magnetisation, or simply magnetisation of a magnetised substance represents the extent to which the substance is magnetised. It is defined as the magnetic moment per unit volume of the magnetised substance and is denoted by \[\vec M\].
Numerically, \[\vec M\] = \[\frac {\vec m}{V}\]
SI unit: (A m-1)
Definition: Magnetic Intensity or Magnetic Field Strength
The magnetic intensity \[\vec H\] is defined through the vector relation \[\vec H\] = \[\frac{\overrightarrow{B}}{\mu_{0}}-\overrightarrow{M}\], where \[\vec B\] is magnetic field induction inside the substance and \[\vec M\] is the intensity of magnetisation. μ0 is permeability of free space.
Definition: Magnetic Permeability
It is defined as the ratio of the magnetic induction \[\vec B\] inside the magnetised substance to the magnetic intensity \[\vec H\] of the magnetising field.
Numerically, μ = \[\frac {B}{H}\]
SI unit: newton/ampere² (NA2), or tesla-metre/ampere (TmA-1), or weber/ampere-metre (Wb A-1m-1).
Definition: Relative Magnetic Permeability
The relative magnetic permeability of a substance is the ratio of the magnetic permeability u of the substance to the permeability of free space μo, that is,
μr = \[\frac{\mu}{\mu_0}\]
Definition: Relative Permeability
The relative permeability of a substance is defined as the ratio of the magnetic flux density B in the substance when placed in a magnetic field and the flux density B0 in vacuum in the same field,
\[\mu_r=\frac{B}{B_0}\]
Definition: Curie Temperature
The temperature above which a ferromagnetic substance becomes paramagnetic is called the 'Curie temperature' of the substance. The Curie temperature of iron is 770°C and that of nickel is 358°C.
Definition: Retentivity
The retentivity of a substance is a measure of the magnetisation remaining in the substance when the magnetising field is removed.
Definition: Coercivity
The coercivity of a substance is a measure of the reverse magnetising field required to destroy the residual magnetism of the substance.
Definition: Hysteresis Loss
The energy lost per unit volume of a substance in a complete cycle of magnetisation is equal to the area of the hysteresis loop (M-H curve).
Definition: Residual Magnetism
The magnetisation remaining in the substance when the magnetising field is reduced to zero is called the "residual magnetism".
Formulae [4]
Formula: Torque on Magnetic Dipole
\[\tau=MB\sin\theta\]
Vector form: \[\vec{\tau}=\vec{M}\times\vec{B}\]
Formula: Magnetic Field on the Axial Line of a Dipole
B = \[\frac{\mu_{0}}{4\pi}\frac{2m}{r^{3}}\]
Formula: Magnetic Field on Equatorial Line of Dipole
B = \[\frac{\mu_0}{4\pi}\frac{m}{r^3}\]
Formula: Angle of Dip
\[\theta=\tan^{-1}\left(\frac{B_{V}}{B_{H}}\right)\]
Theorems and Laws [3]
Law: Law of Hysteresis
When a ferromagnetic material is subjected to a cycle of magnetisation and demagnetisation, the intensity of magnetisation (I) or magnetic induction (B) lags behind the magnetising field (H). This lagging behaviour is called hysteresis. When plotted on a B–H graph, the curve forms a closed loop (hysteresis loop) in which:
- B0 (point A) denotes the saturation magnetic induction,
- The intercept OB (or OC) on the B-axis when H is reduced to zero represents retentivity (residual magnetism),
- The intercept OF on the H-axis (reverse field H0) needed to reduce B to zero represents coercivity,
- Points D and E represent reverse saturation and reverse retentivity respectively.
The area enclosed by the hysteresis loop is equal to the energy loss per cycle per unit volume of the material, and this area is different for different materials. Therefore, materials used as electromagnets require a narrow loop (low hysteresis loss), while permanent magnets require a wide loop (high retentivity and coercivity).
Law: Curie–Weiss Law
For ferromagnetic materials, the variation of Xm with T is very peculiar and follows Curie-Weis law, Xm = \[\left(\frac{C}{T-T_{c}}\right)\] according to which the variation of Xm at low
temperatures less than Tc is very complex but above it the variation becomes as simple as the paramagnetic susceptibility.
Law: Curie’s Law
Statement
In 1895, Curie discovered experimentally that the magnetisation M (magnetic moment per unit volume) of a paramagnetic substance is directly proportional to the magnetic intensity H of the magnetising field and inversely proportional to the Kelvin temperature T, i.e.,
M = C (H/T)
where C is a constant called the Curie constant.
Explanation
The law states that magnetisation depends on both the applied magnetic field and temperature. It holds so long as the ratio H/T does not become too large. Magnetisation cannot increase indefinitely and approaches a maximum value corresponding to the complete alignment of all the atomic magnets in the substance.
Since magnetic susceptibility is defined as
χm = M/H,
eliminating M from the above equations gives
χm = C/T,
or
χm ∝ 1/T.
Conclusion
For paramagnetic substances, the magnetic susceptibility varies inversely with the absolute temperature, and this relation is known as Curie’s Law.
Key Points
Key Points: Current Loop as a Magnetic Dipole
- A current-carrying loop behaves like a magnetic dipole (bar magnet)
- Polarity Rule
Anticlockwise current → North pole (upper face)
Clockwise current → South pole (lower face)
Key Points: Magnetic Torque on a Dipole
- A bar magnet placed in a uniform magnetic field experiences a torque that tends to align its magnetic axis parallel to the field.
- A current loop behaves like a magnetic dipole, and its behaviour in a magnetic field is similar to that of a bar magnet.
- According to the modern theory, a magnet consists of many tiny current loops, and the total torque on the magnet is the sum of torques on these loops.
- The torque depends on the magnet's orientation in the magnetic field and is maximum when the magnetic axis is perpendicular to the field.
- When the magnetic axis is parallel or antiparallel to the magnetic field, the torque becomes zero, and the magnet is in equilibrium.
Key Points: Magnetic Dipole Moment of a Revolving Electron
- An electron revolving around the nucleus behaves like a tiny current loop and hence acts as a magnetic dipole.
- The magnetic dipole moment of a revolving electron arises due to its orbital motion and is perpendicular to the plane of the orbit.
- The direction of magnetic dipole moment is opposite to the direction of the electron’s orbital angular momentum.
Key Points: Properties of Magnetic Lines of Force
- Magnetic lines of force emerge from the north pole, enter the south pole, and return to the north pole, forming closed, continuous loops.
- No two magnetic lines of force ever intersect, because intersection would imply more than one direction of the magnetic field at a point, which is impossible.
- The density of magnetic lines of force represents field strength; lines are closer near the poles, where the field is strong, and farther apart where the field is weak.
- In a uniform magnetic field, such as the Earth’s magnetic field at a place, the lines of force are parallel and equally spaced.
- Magnetic lines of force do not pass through a neutral point and may enter or leave a magnetic pole at any angle.
Key Points: Equivalence of Solenoid and Bar Magnet
- Two current-carrying solenoids show attraction and repulsion; unlike poles attract each other, while like poles repel each other.
- The polarity of a solenoid is determined by the end rule: anti clockwise current at an end indicates a north pole, and clockwise current indicates a south pole.
- The far axial magnetic field of a finite solenoid is
B = \[\frac{\mu_{0}}{4\pi}\frac{2m}{r^{3}}\],
which is the same as the axial magnetic field of a bar magnet, proving their magnetic equivalence.
Key Points: Magnetic Dipole of a Current Loop
- A current-carrying loop behaves like a magnetic dipole, similar to a bar magnet.
- When placed in a uniform magnetic field, a current loop experiences a torque that tends to align its axis parallel to the field.
- By comparing the torque on a current loop with that on an electric dipole, the magnetic dipole moment of a current loop is defined as m = I A.
- The direction of the magnetic dipole moment is perpendicular to the plane of the loop and is given by the right-hand curled-finger rule.
- For a coil having N turns, the magnetic dipole moment is
m = N I A, and its SI unit is A·m².
Key Points: Terms Used in Magnetism
| Quantity | Symbol | Definition | Formula | Unit | Nature |
|---|---|---|---|---|---|
| Magnetising Field (Magnetic Field Intensity) | H | Measure of the external magnetic field applied to a material | \[H=\frac{B}{\mu}\] | A/m | Vector |
| Intensity of Magnetisation | I | Magnetic dipole moment per unit volume | \[I=\frac{M}{V}\] | A/m | Vector |
| Magnetic Susceptibility | \[\chi_{m}\] | Ratio of magnetisation to magnetising field | \[\chi_m=\frac{I}{H}\] | No unit | Scalar |
| Magnetic Permeability | \[\mu\] | Ratio of magnetic field to magnetising field | \[\mu=\frac{B}{H}\] | H/m (or T·m/A) | Scalar |
| Relative Permeability | \[\mu_{r}\] | Ratio of permeability of medium to free space | \[\mu_r=\frac{\mu}{\mu_0}\] | No unit | Scalar |
Key Points: Difference in Magnetic Properties of Soft Iron and Steel
- The retentivity of soft iron is greater than that of steel.
- The coercivity of soft iron is less than the coercivity of steel.
- The hysteresis loss in soft iron is smaller than in steel because the area of its hysteresis loop is smaller.
- Steel has a larger hysteresis loop area than soft iron, indicating greater energy loss per cycle.
- The permeability of soft iron is greater than that of steel, as shown by the B − H curves.
Key Points: Selection of Magnetic Materials
- Permanent magnets need high retentivity and high coercivity, so steel is used.
- Electromagnets need high permeability and low retentivity, so soft iron is used.
- Transformer cores and telephone diaphragms must have low hysteresis loss to reduce heating.
- Soft iron and special alloys (permalloys, µ-metals) are preferred for efficient magnetic performance.
Key Points: Properties of Dia-, Para- and Ferromagnetic Substances
- Diamagnetic substances are weakly magnetised opposite to the applied magnetic field.
- In a magnetic field, a diamagnetic rod aligns perpendicular, while a paramagnetic and ferromagnetic rod aligns parallel to the field.
- In a non-uniform magnetic field, diamagnetic substances move from stronger to weaker regions, whereas paramagnetic substances move from weaker to stronger regions.
- Diamagnetic liquids are depressed in regions of strong magnetic fields, while paramagnetic liquids rise in regions of strong magnetic fields.
- Diamagnetic gases spread across the magnetic field, whereas paramagnetic gases spread along the field.
- Ferromagnetic substances exhibit strong magnetisation even in weak magnetic fields and have high permeability.
- Ferromagnetic substances exhibit magnetic hysteresis and lose their ferromagnetic nature above a certain temperature.
Important Questions [3]
- Define Curie temperature.
- If Magnetic Susceptibility of a Certain Magnetic Material is 0 0001, Find Its Relative Permeability.
- A Rectangular Loop of Area 5m2, Has 50 Turns and Carries a Current of 1a. It is Hold in a Uniform Magnetic Field of 0.1t, at an Angle of 30°. Calculate the Torque Experienced by the Coil.
Concepts [20]
- Current Loop as a Magnetic Dipole
- Magnetic Dipole Moment of a Revolving Electron
- Magnetic Field of a Magnetic Dipole (Small Bar Magnet)
- Torque on a Magnetic Dipole (Bar Magnet) in a Uniform Magnetic Field
- Potential Energy of a Magnet in a Magnetic Field
- Current-Carrying Solenoid as an Equivalent to a Bar Magnet
- Magnetic Lines of Force
- Earth’s Magnetic Field
- Elements of the Earth's Magnetic Field > Angle of Declination
- Elements of the Earth's Magnetic Field > Angle of Dip or Magnetic Inclination
- Elements of the Earth's Magnetic Field > Horizontal Component of Earth's Magnetic Field
- Overview: Magnetic Field and Earth's Magnetism
- Classification of Substances According to their Magnetic Behaviour
- Terms Used in Magnetism
- Properties of Dia-, Para-, and Ferromagnetic Substances
- Explanation of Dia-, Para-, and Ferromagnetism based on the Atomic Model of Magnetism
- Hysteresis: Retentivity and Coercivity
- Differences in Magnetic Properties of Soft Iron and Steel
- Magnetic Materials
- Overview: Magnetic Classification of Substances
