Magnetic Properties of Materials
Class 12 Physics Notes • NEB Syllabus 2083
Hysteresis diagram, dia-, para- and ferromagnetic materials with examples, 10 solved multiple choice questions, step-by-step numericals, handwritten and typed PDF notes and frequently asked questions.
1. Syllabus
Unit: Electricity and Magnetism
Chapter 17: Magnetic Properties of Materials (3 hours)
17.1 Magnetic field lines and magnetic flux
17.2 Flux density in magnetic material; relative permeability; susceptibility
17.3 Hysteresis
17.4 Dia-, para- and ferromagnetic materials
These notes follow the NEB Class 12 Physics syllabus (+2 Physics, Nepal). Read the quick overview first, practise the multiple choice questions, then work through the numericals, and finish with the PDF notes for quick revision.
2. Magnetic Properties at a Glance
The magnetic properties of a material describe how it responds to an applied magnetic field. They are measured by the relative permeability \(\mu_r\) and the susceptibility \(\chi\), and they divide materials into diamagnetic, paramagnetic and ferromagnetic substances.
Magnetic field lines and flux
Magnetic field lines are imaginary lines whose tangent at any point gives the direction of the field. They form closed loops (north to south outside a magnet, south to north inside), are closer together where the field is stronger, and never intersect. Magnetic flux is
where \(\theta\) is the angle between \(\vec B\) and the normal to the area. The net flux through a closed surface is zero.
Flux density in a magnetic material
| Quantity | Relation |
|---|---|
| Magnetising field (solenoid) | \(H=nI\) |
| Flux density in the material | \(B=\mu_0(H+M)\) |
| Susceptibility | \(\chi=\dfrac MH\) (no unit) |
| Relative permeability | \(\mu_r=\dfrac{\mu}{\mu_0}=1+\chi\) |
| Flux density and \(H\) | \(B=\mu_0\mu_rH\) |
Hysteresis loop
Figure: B-H hysteresis loop of a ferromagnetic material. The area of the loop is the energy lost per unit volume per cycle.
Hysteresis is the lagging of the flux density \(B\) behind the magnetising field \(H\). The value of \(B\) left when \(H=0\) is the retentivity \(B_r\); the reverse field needed to bring \(B\) to zero is the coercivity \(H_c\). Soft materials (soft iron) have low coercivity and a narrow loop, and are used for transformer cores and electromagnets. Hard materials (steel, alnico) have high coercivity and a wide loop, and are used for permanent magnets.
Diamagnetic, paramagnetic and ferromagnetic materials
| Property | Diamagnetic | Paramagnetic | Ferromagnetic |
|---|---|---|---|
| Behaviour in a field | Weakly repelled | Weakly attracted | Strongly attracted |
| Susceptibility \(\chi\) | Small, negative (about \(-10^{-5}\)) | Small, positive | Large, positive |
| Relative permeability \(\mu_r\) | Slightly less than 1 | Slightly more than 1 | Much greater than 1 |
| Atomic dipoles | None permanent; a small one is induced opposite to the field | Permanent, randomly oriented | Permanent, aligned in domains |
| Effect of temperature | Almost none | \(\chi\propto1/T\) (Curie’s law) | \(\chi\) falls with \(T\); becomes paramagnetic above the Curie temperature |
| Examples | Bismuth, copper, gold, silver, water | Aluminium, platinum, sodium, manganese, oxygen | Iron, cobalt, nickel, alnico |
3. Multiple Choice Questions
Question 1. A permanent magnet is made from which one of the following substances?
- a) Diamagnetic
- b) Paramagnetic
- c) Ferromagnetic
- d) Soft iron
Correct Answer: c) Ferromagnetic
Reason: A permanent magnet must keep a strong magnetic field after the magnetising field is removed. Ferromagnetic materials (hard steel, alnico) have aligned domains, high retentivity and high coercivity. Soft iron is also ferromagnetic but has very low coercivity, so it is used for temporary electromagnets, not permanent magnets.
Question 2. At a certain place the horizontal component of the Earth’s magnetic field is \(B_0\) and the angle of dip is \(45^\circ\). What will be the total intensity of the field at that place?
- a) \(B_0\)
- b) \(\sqrt2\,B_0\)
- c) \(2B_0\)
- d) \(B_0^2\)
Correct Answer: b) \(\sqrt2\,B_0\)
Reason: The horizontal component is \(B_H=B\cos\delta\):
Question 3. Where does the Earth’s magnetic field not have a horizontal component?
- a) At the equator
- b) At a magnetic pole
- c) At a latitude
- d) At a longitude of \(60^\circ\)
Correct Answer: b) At a magnetic pole
Reason: At a magnetic pole the field lines are vertical, so the angle of dip is \(\delta=90^\circ\) and \(B_H=B\cos90^\circ=0\).
Question 4. How can a magnetic field be detected?
- a) It always exerts a force on a charged particle
- b) It never exerts a force on a charged particle
- c) It exerts a force on a moving charged particle moving along the magnetic field
- d) It exerts a force on a moving charged particle moving at an angle to the magnetic field
Correct Answer: d) It exerts a force on a moving charged particle moving at an angle to the magnetic field
Reason: The magnetic force is \(\vec F=q(\vec v\times\vec B)\). It exists only if the charge is moving and its velocity is not parallel (or antiparallel) to \(\vec B\). A charge moving at an angle to the field is deflected, which reveals the field.
Question 5. What happens to the susceptibility of a ferromagnetic substance when the temperature is increased?
- a) Increases
- b) Decreases
- c) Remains constant
- d) Can increase or decrease
Correct Answer: b) Decreases
Reason: Higher temperature increases thermal agitation, which disturbs the parallel alignment of the domains. The material is then magnetised less easily, so its susceptibility decreases.
Question 6. The magnetic susceptibility of a diamagnetic substance is:
- a) Large and positive
- b) Small and positive
- c) Small and negative
- d) Zero
Correct Answer: c) Small and negative
Reason: A diamagnetic material develops an induced magnetisation opposite to the applied field, so its susceptibility \(\chi\) is small and negative (of the order of \(-10^{-5}\)), and \(\mu_r\) is slightly less than 1.
Question 7. Magnetic lines of force:
- a) Cannot intersect at all
- b) Intersect at infinity
- c) Intersect within the magnet
- d) Intersect at the neutral point
Correct Answer: a) Cannot intersect at all
Reason: A field line gives the direction of the field at each point. If two lines crossed, a compass needle at the crossing would have to point in two directions at once, which is impossible. So magnetic field lines never intersect.
Question 8. What is the temperature above which a ferromagnetic material becomes paramagnetic called?
- a) Critical temperature
- b) Inversion temperature
- c) Curie temperature
- d) Debye temperature
Correct Answer: c) Curie temperature
Reason: Above the Curie temperature \(T_C\), thermal agitation destroys the domain alignment and the ferromagnetic material behaves as a paramagnetic material.
Question 9. What is the cause of the Earth’s magnetic field?
- a) Motion and distribution of conducting material (molten iron and nickel) inside the Earth
- b) Interaction of cosmic rays with the currents of the Earth
- c) A magnetic dipole buried at the centre of the Earth
- d) Induction effect of the Sun
Correct Answer: a) Motion and distribution of conducting material (molten iron and nickel) inside the Earth
Reason: According to the dynamo theory, convection currents of molten iron and nickel in the outer core, together with the Earth’s rotation, produce circulating electric currents that generate the magnetic field. A buried dipole is only a convenient model.
Question 10. A magnet of dipole moment 2 A m² is deflected through \(30^\circ\) from the magnetic meridian. The required deflecting torque is (\(B_H=0.4\times10^{-4}\ \mathrm{T}\)):
- a) \(0.4\times10^{4}\ \mathrm{N\,m}\)
- b) \(0.4\ \mathrm{N\,m}\)
- c) \(0.4\times10^{-4}\ \mathrm{N\,m}\)
- d) \(0.8\times10^{-4}\ \mathrm{N\,m}\)
Correct Answer: c) \(0.4\times10^{-4}\ \mathrm{N\,m}\)
Reason: The magnetic meridian is along \(B_H\), so
4. Numerical and Subjective Questions
a) What are magnetic field lines? State their properties.
Magnetic field lines are imaginary lines drawn so that the tangent at any point gives the direction of the magnetic field there.
Properties: they form closed loops (from north to south outside a magnet and from south to north inside it); the number of lines per unit area is larger where the field is stronger; the tangent at a point gives the direction of the field; and two field lines never intersect, because the field cannot have two directions at one point.
b) Define magnetic flux and state its SI unit. A circular coil of radius 0.1 m is placed in a uniform magnetic field of 0.5 T so that the normal to the coil makes an angle of \(60^\circ\) with the field. Find the flux through the coil.
Magnetic flux is the number of magnetic field lines passing through a surface, \(\Phi=BA\cos\theta\), where \(\theta\) is the angle between \(\vec B\) and the normal to the surface. Its SI unit is the weber (Wb), \(1\ \mathrm{Wb}=1\ \mathrm{T\,m^2}\).
a) Define magnetising field \(H\), magnetisation \(M\), susceptibility \(\chi\) and relative permeability \(\mu_r\). Write the relations among them.
Magnetising field \(H\): the field produced by the free current alone; for a solenoid \(H=nI\).
Magnetisation \(M\): the magnetic dipole moment per unit volume of the material.
Susceptibility \(\chi\): the ratio \(\chi=\dfrac MH\); it has no unit.
Relative permeability \(\mu_r\): the ratio \(\mu_r=\dfrac\mu{\mu_0}\) of the permeability of the material to that of free space.
b) A solenoid has 800 turns per metre and carries a current of 0.5 A. It is filled with an iron core of relative permeability 1200. Find \(H\), \(B\) and \(M\).
a) What is hysteresis? Explain the hysteresis loop and define retentivity and coercivity.
Hysteresis is the lagging of the flux density \(B\) behind the magnetising field \(H\) when a ferromagnetic material is taken through a cycle of magnetisation. Starting from an unmagnetised state, \(B\) rises along the initial curve to saturation as \(H\) increases. When \(H\) is reduced to zero, \(B\) does not return to zero but keeps the value \(B_r\), the retentivity (remanence). A reverse field \(H_c\), the coercivity, is needed to bring \(B\) to zero. Carrying \(H\) through a full cycle traces a closed B-H loop.
b) What does the area of the loop represent? The area of the B-H loop of a transformer core is 150 J m\(^{-3}\) per cycle. Find the energy lost in a core of volume 0.02 m\(^3\) in one hour when the supply frequency is 50 Hz.
The area of the B-H loop equals the energy lost as heat per unit volume of the material in one cycle of magnetisation.
c) Why is soft iron used for transformer cores and steel for permanent magnets?
Soft iron has high permeability, low coercivity and a narrow hysteresis loop, so it is easily magnetised and demagnetised with very little energy loss. This suits transformer cores and electromagnets, where the field changes continually.
Steel has high coercivity and high retentivity, with a wide loop. It keeps its magnetism once magnetised and is not easily demagnetised, which suits permanent magnets.
a) Differentiate between diamagnetic, paramagnetic and ferromagnetic materials with examples.
| Basis | Diamagnetic | Paramagnetic | Ferromagnetic |
|---|---|---|---|
| In a magnetic field | Weakly repelled; moves toward the weaker field | Weakly attracted; moves toward the stronger field | Strongly attracted |
| \(\chi\) | Small, negative | Small, positive | Large, positive |
| \(\mu_r\) | Slightly below 1 | Slightly above 1 | Much greater than 1 |
| Examples | Bismuth, copper, water | Aluminium, platinum, oxygen | Iron, cobalt, nickel |
b) What is the Curie temperature? The susceptibility of a paramagnetic material at 300 K is \(1.2\times10^{-5}\). Find its susceptibility at 400 K.
The Curie temperature is the temperature above which a ferromagnetic material loses its ferromagnetism and becomes paramagnetic, because thermal agitation destroys the domains.
For a paramagnetic material Curie’s law gives \(\chi\propto\dfrac1T\):
a) Explain ferromagnetism using the domain theory.
A ferromagnetic material is divided into small regions called domains. In each domain the atomic magnetic dipoles are all aligned in one direction, so each domain is strongly magnetised. In an unmagnetised sample the domains point in random directions and their effects cancel. When an external field is applied, domains aligned with the field grow and others rotate toward the field direction, so the material develops a large magnetisation. When all the domains are aligned, the material is saturated.
b) Why does a ferromagnetic material become paramagnetic when heated above its Curie temperature?
At high temperature the thermal agitation of the atoms is strong enough to overcome the forces that align the dipoles within a domain. The domains break up and the dipoles become randomly oriented, so the material behaves as a paramagnetic substance.
5. View PDF Notes
i. Handwritten Notes
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6. Frequently Asked Questions
What are the magnetic properties of materials?
What are magnetic field lines and what are their properties?
What is magnetic flux?
What are relative permeability and magnetic susceptibility?
What is the formula for flux density in a magnetic material?
What is hysteresis?
What is the difference between soft and hard magnetic materials?
What are diamagnetic materials? (with examples)
What are paramagnetic materials? (with examples)
What are ferromagnetic materials and what is the Curie temperature?
How does temperature affect magnetic susceptibility?
What is magnetic properties in chemistry?
What are examples of magnetic materials?
What topics are included in Chapter 17 Magnetic Properties of Materials of NEB Class 12 Physics?
Where can I get Class 12 Physics Magnetic Properties of Materials notes in PDF?
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