Chapter 7 – Magnetic Properties – Applied Physics

CHAPTER 7

Magnetic Properties

7.1 Magnetic permeability

Magnetic permeability represents the ease with which a material allows magnetic force of lines to pass through it. The permeability of vacuum or free space is denoted by μ0 and it is taken as the standard with respect to this the permeability of all materials is expressed. The permeability of the medium of a material is denoted as μ; it is the product of the permeability of free space (μ0) and relative permeability (μr).

 

 

μr is purely a number; it has no units. The permeability of free space is:

 

 

Let B be the magnetic flux density in a magnetic material by applying magnetic field of intensity H and B0 be the flux density at the same place if the material is removed [i.e., in air or vacuum]. Then, B0 α H

 

 

Similarly,

 

 

Dividing Equation (7.2) by Equation (7.1)

 

 

Therefore, the relative magnetic permeability of a material is defined as the ratio of magnetic flux density [or magnetic induction] in a material to that in vacuum under the same applied magnetic field. The magnetic induction is the magnetic flux over unit area of a surface held normal to the flux. It is denoted by B and its SI unit is Tesla [Tesla = Wb/m2]. The SI unit of magnetic field strength H is A/m and that of μ is wb/A-m or H/m. The Maxwells equations exhibit that the speed of light in a medium

In vacuum, where ε0 and ε are the permittivity of free space and permittivity in a material medium respectively

7.2 Magnetization (M)

A magnetic material acquires magnetism in an applied magnetic field. The magnetization is due to the rotation of magnetic dipoles of atoms or molecules of the substance in the direction of the applied magnetic field. The magnetic dipole moment per unit volume of the material is called intensity of magnetization or simply magnetization (M).

 

 

The magnetic flux density or magnetic induction (B) inside the material is directly proportional to the applied magnetic field (H) on the material.

i.e.,

 

 

where μ = magnetic permeability of the material, Equation (7.4) can be written as:

 

 

The magnetic induction inside the material is due to the applied field H and due to magnetization M of the material.

So,

 

 

Comparing Equations (7.5) and (7.6), we have:

 

 

Equation (7.5) indicates that the magnetic flux density in a magnetic material by applied magnetic field is equal to the sum of the effect on vacuum and that on the material. The ratio of magnetization (M) to the applied magnetic field strength (H) is called the magnetic susceptibility (x) of the material.

 

 

Using Equation (7.7),

 

7.3 Origin of magnetic moment—Bohr magneton—electron spin

We know that electric current through a conductor develops magnetic field around it or current through a coil of wire will act as a magnet. This informs that there is an intimate relation between electric current and magnetic field. Flow of electrons along a path constitute electric current. In all atoms, electrons are revolving around the nucleus in different orbits. These revolving electrons constitute an electrical current in the orbits. These currents form magnetic dipoles. As electrons in an atom are revolving in different orbits that are randomly oriented, so the magnetic dipoles due to orbital motion of electrons are randomly oriented, results in zero magnetic dipole moment. The spin of orbital electrons and the spin of nucleus also contribute to the magnetic effects to an atom. Under an external applied magnetic field, these dipoles experience torque in the direction of the applied field and the atom acquires certain magnetism. Therefore, the magnetic dipole moment of an atom is due to the orbital motion of electrons, spin of electrons and spin of nucleus. We will study these contributions in detail separately.

(i) Magnetic moment due to orbital motion of electrons and orbital angular momentum

As shown in Fig. 7.1, let an electron moving with a constant speed ‘υ’ along a circular orbit of radius ‘r’. Let ‘T ’ be the time taken to complete one revolution and –e be the charge on an electron. The charge that crosses any reference point in the orbit in unit time is and this is equal to current in the orbit. So, current in the orbit:

 

 

Figure 7.1 Orbital angular momentum of an electron

 

The magnetic moment (μl) associated with the orbit due to orbital motion of electron is:

 

 

where    A = area of the orbit = πr2

Equation (7.9) becomes:

 

 

The angular velocity,

 

 

Substituting Equation (7.11) in Equation (7.10), we have:

 

 

Since linear velocity (v)=

Multiplying and dividing Equation (7.12) with mass of electron, me

 

 

where L = orbital angular momentum of the electron.

The negative sign in Equation (7.13) indicates that the angular momentum vector and magnetic momentum vector are in opposite direction. In quantum theory, the angular momentum is expressed as

 

 

Where l = 0, 1, 2, 3, etc. for s, p, d, f, etc. electrons and

Substituting Equation (7.14) in Equation (7.13), we get:

 

 

In the above equation, the quantity is an atomic unit called Bohr magneton represented as a μB and its value is equal to 9.27 × 10-24 A–m2.

 

 

In many substances, the orbital magnetic moment of one electron in an atom gets cancelled by the orbital magnetic moment of other electron revolving in opposite direction in the same atom. Thus, the resultant magnetic dipole moment of an atom and in turn the substance is zero or very small.

(ii) Magnetic moment due to spin of the electrons

In addition to orbital motion, the electrons spin around its own axis. The magnetic moment due to the spin of electrons is represented as μs. This is analogous to Equation (7.13), in which orbital angular momentum is replaced by the spin angular momentum ‘S’ given by:

 

 

where γ is called spin gyromagnetic ratio and it is defined as the ratio of the magnetic dipole moment to the angular momentum of an electron. The experimental value of γ for an electron is –2.0024. According to quantum theory, the spin angular momentum of an electron (S) is The magnetic moment due to the spin of the electron is given by:

 

 

Substituting these values in the above equation:

μs = 9.4 × 10–24 A–m2

The magnetic moments due to the spin and the orbital motions of an electron are of the same order of magnitude.

If the atoms of a material consist of an even number of electrons, then the spin magnetic moments of pairs of electrons get cancelled due to the opposite spin. On the other hand, if the material consists of an odd number of electrons, then at least one electron remains unpaired and this leads to the magnetic moment of the atoms.

(iii) Magnetic moment due to nuclear spin

Similar to electrons, the protons present in nucleus possess spin; the vectorial sum of all the protons spins is equal to the nuclear spin. The magnetic moment of a nucleus is expressed as nuclear magneton (μn) given as:

 

 

where mp = mass of a proton.

The value of μn is equal to 5.05 × 10-27 A-m2. Since mass of a proton is nearly 2000 times heavier than an electron, so μn is very small compared to μB and it can be neglected. Therefore, the total magnetic moment of an atom will be mainly the vectorial sum of the orbital and spin magnetic moments of electrons.

7.4 Classification of magnetic materials

By the application of magnetic field, some materials will not show any effect that are called non-magnetic materials and those which show some effects are called magnetic materials. All magnetic materials magnetizes in an applied external magnetic field. Depending on the direction and magnitude of magnetization and also the effect of temperature on magnetic properties, all magnetic materials are classified into dia, para and ferromagnetic materials. Two more classes of materials have structure very close to ferromagnetic materials, but possess quite different magnetic properties. They are anti-ferromagnetic and ferrimagnetic materials. The properties of these materials are described below.

(i) Diamagnetic material

Diamagnetic materials are repelled by the applied magnetic fields and they magnetize to a small extent in the opposite direction to that of an applied external magnetic field. The magnetic susceptibility is small and negative for these materials. Magnetic susceptibility represents the ease of magnetization of a substance and is equal to the ratio of magnetization of a material to the applied magnetic field. The relative permeability (μr) is less than 1 for these materials. Examples are gold, copper, silver, bismuth, lead, zinc and noble gases.

(ii) Paramagnetic materials

These materials are feebly attracted by external magnetic fields and they magnetize in the direction of the applied magnetic field. The magnetic susceptibility is small and positive. The relative permeability is greater than 1 for these materials. Paramagnetism is due to the spin and orbital, motion of the electrons. Examples are aluminium, platinum, manganese chloride, salts of iron, nickel, tungsten and nitrogen.

(iii) Ferromagnetic materials

These materials are strongly attracted by magnetic fields and they magnetize in the direction of the applied external magnetic field. The magnetic susceptibility is positive and large. The relative permeability is greater than 1 for these materials. The atoms or molecules of ferromagnetic materials have magnetic dipole moment due to the spin of the electrons. The permanent magnetic dipoles are all shown in Fig. 7.2(a). Examples are iron, cobalt, nickel and their alloys, Gadolinium and Dysprosium.

 

Figure 7.2 Magnetic dipole moments for adjacent atoms of (a) Ferro; (b) Antiferro and (c) Ferrimagnetic substances

(iv) Anti-ferromagnetic materials

Antiferromagnetic materials show very little external magnetism. Magnetic susceptibility of these materials is positive and small. The atoms or molecules of anti-ferromagnetic materials possess magnetic dipole moment due to the spin of electrons. The magnetic dipole moments of adjacent atoms are anti-parallel as shown in Fig. 7.2(b). Due to the anti-parallel magnetic dipole moments, the magnetic effect of an anti-ferromagnetic material is zero, but possess magnetism due to temperature-dependent disruption of the magnetic moment alignment. Examples are copper chloride, oxides of manganese, cobalt and nickel.

(v) Ferrimagnetic materials [Ferrites]

The magnetization of ferrimagnetic materials is intermediate to that of ferromagnetic and anti-ferromagnetic materials. The magnetic susceptibility is large and positive. The magnetic dipole moments of adjacent atoms or molecules of ferrimagnetic materials are anti-parallel and unequal in magnitude as shown in Fig. 7.2(c). This unequal magnetic dipole moments of adjacent atoms result in a net magnetization in the material. Examples are all ferrites have a general formula MOFe2O3, in which M stands for any divalent ion, for example copper, zinc, cadmium, iron, cobalt, nickel, etc.

7.5 Classical theory of diamagnetism [Langevin theory]

In this theory, we will obtain an expression for the change in magnetic moment of an orbiting electron in a diamagnetic atom and the induced magnetic moment per unit volume of diamagnetic material in the applied magnetic field B0.

A revolving electron in an orbit constitutes electric current in the orbit. This electric current produces magnetic field perpendicular to the plane of the orbit. The electrons in an atom are revolving in different orbits, oriented in random directions. So, the sum of the magnetic moments produced by all these orbiting electrons in an atom is zero. Let the angular velocity of an electron in an orbit of radius ‘r’ is ‘ω0’ before applying magnetic field. The current in the orbit is [since v0 = 0]. The magnetic moment due to the orbiting electron

 

 

 

where A is the area inside the orbit. As shown in Figs. 7.3(a) and (b), the electrostatic force of attraction (Fe) between a proton and an orbiting electron constitutes centripetal force on the electron and it is equal to

 

 

where v0 = linear velocity of the electron.

 

 

After applying magnetic field B0, an additional force FB acts on the electron. Depending on the direction of the applied magnetic field and depending on the direction of rotation of electron, the force FB either adds to Fe or reduces Fe. Let the centrifugal force after applying magnetic field be F (= m2), where ω = ω0 ± Δω, Δω = change in the angular frequency of electron after applying magnetic field.

Then, we have:

 

 

The additional force is equal to:

 

 

 

Equation (7.22) becomes:

mrω2 = mrω20 ± B0erω

 

Figure 7.3 (a) Electron revolving in an orbit of radius ‘r’ around a proton in the absence of an external magnetic field; (b) Electron revolving in an orbit of radius ‘r ’ around a proton in the presence of applied magnetic field B0

 

 

 

2 = mω0 ± B0

or:

 

 

 

 

 

 

Neglecting ∆ω2, we have:

 

 

The change in magnetic moment (∆μl) for the change in angular frequency (∆ω) is obtained using Equations (7.20) and (7.25)

 

 

The induced dipole moment has a direction opposite to the applied magnetic field. The magnetic moment induced when a pair of electrons have opposite rotation is:

 

 

This induced magnetic moment is in the opposite direction to B0. This is the property of a diamagnetic material. Diamagnetic atoms have more than one electron and the orbits are also not circular. Suppose rx, ry, and rZ are the average values of radii of all electrons along three directions, then radius of the atom (ro) is:

ro2=rx2+ry2+rz2  also if  rx2=ry2=rz2=

The average radius of the orbit

 

 

Suppose the diamagnetic substance contains N atoms per unit volume and each atom has z electrons, then the induced magnetic moment per unit volume (µind) is:

 

 

since B0 = µ0 H

 

 

So,

The atomic susceptibility,

 

 

The value of X of the order of 10−6.

7.6 Theory of paramagnetism

The atoms of paramagnetic material possess permanent magnetic moment. In the absence of an applied external magnetic field, the magnetic dipoles of paramagnetic atoms are oriented in random directions, so that there is no resultant magnetism of the material. By applying an external magnetic field on a paramagnetic material, the dipoles are rotated by different extents proportional to the strength of field in the direction of the applied magnetic field, so that the material acquires magnetism.

To calculate magnetic susceptibility, we consider N number of magnetic dipoles per unit volume of material of which Np dipoles are parallel to the applied field and Na dipoles are anti-parallel when a magnetic field H applied at temperature T K.

The net magnetization of the material, M =NpµBNaµB

 

 

where  μB = Bohr magneton =

Also the magnetic susceptibility

 

 

The torque (τ) experienced in the applied magnetic field is:

 

 

where μm is the moment of magnetic dipole. Figure (7.4) shows the energy difference between parallel and anti-parallel spin dipoles.

 

Figure 7.4 Energy difference between parallel and anti-parallel magnetic dipoles

 

Consider the energy θ of a dipole is zero when it is perpendicular to the field. The energy of dipole when it makes an angle θ to the field is:

 

 

Enegy of anti-parallel dipole is obtained by putting θ = 180°

i.e., Ea = µ0µm H

Similarly, energy of parallel dipole is obtained by putting θ=0°

i.e., Ep = ―µ0µm H

 

 

For a single spin moment, μm = μB

 

 

Using Boltzmann statistics, the ratio is given by:

 

 

Using Equation (7.36)

 

 

To obtain Na and Np separately in terms of N, consider:

 

 

Hence,

 

 

 

similarly,

 

 

Hence,

 

 

Substituting the above equation in Equation (7.32), we have:

The net magnetization

 

 

where

In Fig. 7.5,is plotted against the variable, α

 

Figure 7.5 The solid curve represents M/N μB as a function of α = μ0μB H/KBT. A dotted line through the origin of slope unity corresponds to α << 1, tan h(α) α

 

α = μ0μBH/KBT for α << 1, tan h (α) ≌ α and for α >> 1, tan h (α) approaches unity. So, for strong fields at low temperatures, the magnetization approaches NμB i.e., the dipoles are aligned parallel to the applied field. For low field at normal temperatures, μ0μBH << KBT, under these conditions α << 1 so tan h (α) ≌ α.

Hence,

 

 

 

where = Curie constant

Hence, we find that the susceptibility varies as

The above equation is known as Curie law of paramagnetism.

7.7 Domain theory of ferromagnetism

In 1907, Weiss proposed domain theory to explain ferromagnetism. According to this theory, a single crystal of ferromagnetic solid compresses a large number of small regions, and each region is spontaneously magnetized to saturation extent called a domain as shown in Fig. 7.6. The domain size may vary from 10–6 to the entire volume of the crystal. The spin magnetic moments of all the atoms in a domain are oriented in a particular direction. The magnetization directions of different domains of the specimen are random so that the resultant magnetization of the material is zero in the absence of an external magnetic field. These domains arise because the energy is not minimum when a large specimen has a uniform magnetization.

 

Figure 7.6 Ferromagnetic domains

 

A ferromagnetic material magnetizes when an external magnetic field is applied. The individual domains contribute to the total magnetization, M, of the specimen. Becker suggested two independent processes by which magnetization of the specimen takes place. They are: (i) the domains that are parallel or nearly parallel to the direction of applied magnetic field will grow in size at the cost of other domains and (ii) the magnetic moments of the domains can rotate in the direction of applied field. A symbolic representation of the response of the domains to the magnetic field is shown in Fig. 7.7.

By the applied magnetic field, either domain wall moments or rotation of domains magnetic moments or both depending on the strength of the applied magnetic field takes place.

If weak magnetic field is applied on a ferromagnetic material, then the domains of the material whose magnetic moments are parallel or nearly parallel to the direction of applied field will expand in size whereas the domains in which magnetic moments are unfavourably oriented to the applied field will diminish in size as shown in Fig. 7.7(b). This change produces large magnetization for the bulk material.

 

Figure 7.7(a) Domain orientation in the absence of magnetic field; (b) Domain enhancement shrikage due to weak fields; (c) Domain rotation due to strong fields; (d) Saturation due to very high fields

 

Application of higher magnetic fields rotates [twists] partially the domain's magnetic moments in the direction of the magnetic field as shown in Fig. 7.7(c). This results in further increase in the magnetization of the bulk material.

Application of very strong magnetic fields on a ferromagnetic material results in required amount of rotation of magnetic moments so as to align parallel to the applied field as shown in Fig. 7.7(d). This is the highest magnetization of the material called saturated magnetization.

Effect of temperature

The Curie–Weiss law for magnetic susceptibility for ferromagnetic substance is:

 

 

where C = Curie constant, θ = Curie temperature and T is the temperature of the ferromagnetic material. Here, ‘θ’ represents the tendency towards alignment of the dipole moments and on the other hand T represents the tendency of random orientation of dipoles due to thermal agitation. For T > θ, the thermal agitation is predominant; so, the substance is paramagnetic. As the temperature (T) is lowered and if comparable to θ, the spin-exchange interaction begins. The temperature at which the spontaneous magnetization sets in is called the Curie temperature.

For all temperatures, T < θ, the material behaves as ferromagnetic.

Experimental evidences for domain structure

One experimental evidence for the existence of magnetic domains was given by Bitter from magnetic powder pattern microphotographs of domain boundaries. In this method, a drop of colloidal solution of ethyl acetate containing a fine powder of magnetic material such as magnetite is put on a carefully prepared [clean and plane] surface of ferromagnetic material. This drop spreads on the surface. When this is observed under the microscope, it is found that the magnetite particles in the suspension are moved and highly concentrated along certain well-defined lines. The ethyl acetate evaporates leaving the particles alone. The magnetite particles are attracted to the lines due to the local inhomogeneity of magnetic field, and the lines indicate change in the magnetic field direction of material. The non-uniformity of magnetite particles on the surface indicates that the material is magnetized in different directions at different regions; such a type of each region is called a domain. This can be photographed. If there are no such domains or the complete material is a single domain, then the magnetization would be uniform all over the surface and no concentration of particles would occur.

Fowler and Fryer described another technique for the existence of magnetic domains. This is described in the following way. The surface of a ferromagnetic material is illuminated with polarized light and viewed through an analyser. The surface appears with areas of different intensity, due to the existence of domains. This can be explained with Kerr magneto-optical effect.

When plane polarized light [electromagnetic waves] incident on the surface of ferromagnetic material, they interact with the magnetic field present at different regions on the surface of material and the plane of polarization is rotated on reflection by different extents at different regions on the surface. Due to the differences in the intensity and direction of magnetic field at different regions, the reflected light appears non-uniform. This confirms the existence of domains.

Origin of [Ferromagnetic] domains

In free state, all physical systems attain minimum energy and that is the condition for stability. On this basis, one can conclude that domains exist in ferromagnetic materials to minimize the total energy of the substance. The total energy of a ferromagnetic solid consists of exchange energy, magnetic field energy, anisotropy energy, domain wall energy and magnetostrictive energy. These energies are described below:

(a) Exchange energy

This is represented as Eex = – 2Je Σ SiSj where Je = total angular momentum quantum number of an electron, Si and Sj are the spin quantum number of ith and jth electrons. This energy is minimum when the spins are parallel.

(b) Magnetic field energy

The magnetic poles formed at the ends of the magnetized specimen produces an external magnetic field. If H is the intensity of magnetic field in a small volume dv, then the magnetic field energy in that volume is . Around the specimen, the intensity of field will be different at different regions. The complete field energy is represented by integration as .

(c) Anisotropy energy

It was experimentally found that much higher fields are required to produce saturated magnetization along certain directions than some other directions in ferromagnetic crystals. They are called hard and easy directions of magnetizations in the crystal. The excess of magnetic field energy required to saturately magnetize the specimen in a direction over that of an easy direction of magnetization is called anisotropy energy in that direction of magnetization. For example, in BCC iron, much higher fields are required to twist the domains to produce saturation magnetization along [111] direction than that of [100] direction. So, [100] direction is the easy direction and that of [111] direction is the hard direction of magnetization in BCC iron. The anisotropy energy is of the order of 105 erg/cm3. In nickel, [111] direction is the easy and [100] direction is the hard direction of magnetization. The anisotropy energy is of 104 erg/cm3. In cobalt, hexagonal crystal axis is the easy direction and [100] is the hard direction of magnetization, and its anisotropy energy is 106 erg/cm3.

(d) Domain wall [or Bloch wall] energy

We know that different domains of a ferromagnetic material magnetizes in different directions. As we go from one domain to its neighbouring domain, the spin [or magnetization] direction does not change abruptly but changes gradually over many atomic planes as shown in Fig. (7.8). So, the spin-exchange energy is lower than when a change occurs abruptly to the same extent. Usually, the domain wall thickness varies from 200 to 300 lattice constants.

(e) Magnetostrictive energy

The change in dimensions of a material on magnetization is called magetostriction. The work done by the magnetic field to produce magnetostriction is stored as energy in the material called energy of magnetostriction or magnetoelastic energy. If the lattice is not strained, then this energy will be zero.

 

Figure 7.8 Shows the change in spin magnetic moment in the domain wall between two domains

 

Explanation for origin of domains

Explanation for the origin of domains is given based on minimization of all the above energies. Suppose the material is magnetized in an easy direction of magnetization so that the anisotropic energy is minimum and let the spin magnetic moments of atoms are parallel so that the exchange energy is minimum and the material compresses as a single domain shown in Fig. 7.9(a). Magnetic poles will be developed at the free ends of the specimen and produce external magnetic fields so that magnetic field energy will be high. To reduce this field energy, let the domain will be sub-divided into two equal domains such that opposite poles at the same end as shown in Fig. 7.9(b), so that field is confined only to a small region near the sample end and magnetic field energy would be reduced to one-half of its previous value. This configuration is at lower energy state than the previous one as shown in Fig. 7.9(c). This process of division leads to lowering of field energy. When the sub-division increases, then the domain wall area and hence the domain wall energy increases. The process of sub-division will be continued [up to n-domains so that the magnetic field energy is reduced to (1/n)th of its initial value] up to a stage at which the decreases in magnetic field energy are equal to the increase in domain wall energy. This is the minimum energy state. With further sub-division, the increase in domain wall energy exceeds the decrease in magnetic field energy. This will not happen because this violates minimum energy configuration. Although the magnetic field energy is reduced considerably by the sub-division, but it is not equal to zero.

There is an arrangement shown in Fig. 7.9(d) for which the magnetic field energy is zero. In this configuration, the magnetization is continuous inside the material so that no free poles are formed anywhere in the material. There is no external magnetic field associated with the magnetization and the magnetic field energy is zero in this case. During the formation of this configuration, the dimensions of the material are changed and this is associated with magnetostrictive strain energy. For example, iron on magnetization, expands in the direction of magnetization and contracts laterally so that the volume remains constant.

 

Figure 7.9 Shows the origin of magnetic domains

 

The magnetostrictive strain energy can be reduced by reducing the size of strain-producing horizontal domains as shown in Fig. 7.9(e). In this configuration, the number of vertical domains increases and also subdivision will be continued until the decrease in magnetostrictive strain energy is compensated by the increase in domain wall energy.

7.8 Hysteresis curve

Hysteresis means retardation or lagging of an effect behind the cause of the effect. In magnetism, hysteresis has been used between the applied magnetic field (H) and magnetization (M) of a magnetic material. Here, the effect is magnetization of a material and the cause of magnetization is the applied magnetic field. Usually, in magnetic materials, the magnetization of a material lags behind the applied magnetic field. This can be explained in detail, in the following way:

We start with an unmagnetized (M = 0) ferromagnetic specimen. With an increasing applied magnetic field on it, the magnetization of the specimen increases from zero to high values. The increase is non-linear. With small applied fields, the domains pointing approximately in the field direction increase at the expense of those that are not. In other words, their boundaries move so as to expand the favourable domains. This gives rise to a small magnetization corresponding to the initial portion of the hysteresis curve shown in Fig. 7.10.

With somewhat higher fields, the magnetization increases rapidly with H. At these field strengths, the boundary moments are often large and irreversible. i.e., the boundaries do not go back into their original position on reducing H. Application of still higher fields, rotates (twists) the magnetization vectors in to the field direction. i.e., all the domains point in the direction of H, then the specimen is said to be saturately magnetized (M = Ms). The saturated magnetization is represented as point ‘P’ in Fig. 7.10. If the field is decreased, then the magnetization decreases below the value Ms, but this decrease of M does not occur along the same path (curve 1), because the domains do not easily return to the original random arrangement. As H is reduced to zero, M does not decrease in phase but lags behind H. The value of M that remains in the material when H is reduced to zero is called residual magnetization or remanence magnetism (Mr).

 

Figure 7.10 Hysteresis curve

 

To remove the residual magnetism in the material, magnetic field is applied in the opposite direction and gradually increased from zero. The magnetization in the material becomes zero for an applied magnetic field of –Hc, called coercive field for the material. Further increase of the applied magnetic field in the opposite direction results in the material magnetization in the opposite direction. Again decreasing the magnetic field in the opposite direction to zero results in the residual magnetism in opposite direction. Again increasing magnetic field in the forward direction, we will get a curve that completes a closed loop called hysteresis loop. This loop includes some area. This area indicates the amount of energy wasted in one cycle of operation.

7.9 Anti-ferromagnetic substances

Anti-ferromagnetism arises when the spin magnetic moments of neighbouring atoms of the crystal are anti-parallel so that the spin magnetic moments of alternate atoms are parallel. Because of opposite spin moments, we consider an anti-ferromagnetic crystal consists of two different types of atoms i.e., say A-type atoms and B-type atoms. The crystal structure consists of interpenetration of two cubic sublattices, one of with A atoms and the other with B atoms. One sub-lattice spontaneously magnetized in one direction and the other in opposite direction. One may therefore suggests the BCC structure for an anti-ferromagnetic crystal with A atoms occupying the corner points and B atoms at the centre of the cubes as shown in Fig. 7.11. Examples are MnO, NiO, FeO, CoO, MnS, etc.

In the absence of an external applied magnetic field, the magnetization of anti-ferro magnetic specimen will be zero, because of anti-parallel and equal spin magnetic moments. By the application of the external magnetic field, a small magnetization in the direction of the applied magnetic field takes place. This magnetization varies with temperature as shown in Fig. 7.12. The susceptibility increases with an increase of temperature up to TN, called the Neel temperature, at Neel temperature the magnetization (or susceptibility) is maximum and above it the magnetization decreases with an increasing temperature, confirming the relation where C = Curie constant and θ is paramagnetic Curie temperature. The decrease of magnetization with an increase of temperature is a property of the paramagnetic substances; therefore, the specimen becomes paramagnetic above TN.

 

Figure 7.11 Opposite magnetic moments of A-type and B-type atoms in the unit cell of antiferromagnetic substance

 

Figure 7.12 Shows the variation of magnetic susceptiblity (X) of antiferromagnetic substance with temperature

 

The variation of magnetic susceptibility with temperature for para, ferro and anti-ferro magnetic materials is shown in Fig. 7.13. In this diagram, a graph has been plotted between versus temperature. For the above materials, the susceptibilities can be expressed as:

 

 

and for anti-ferromagnetic materials.

 

Figure 7.13 Shows the variation of susceptibility with temperature for para, ferro and antiferromagnetic materials

 

7.10 Ferrimagnetic substances [Ferrites]

In ferrimagnetic crystals, the magnetization of two sublattices occurs as the one in anti-ferromagnetic crystals but of unequal magnitudes, which results a non-zero value. The ferrimagnetic crystals consist of two or more different kinds of atoms. Chemically, they are expressed as Me++ Fe2++ O4--, where Me++ stands for a suitable divalent metal ion such as Fe++, Co++, Ni++, Mg++, Mn++, Zn++, Cd++, etc. The Fe2+++is a trivalent ferric ion. If we insert Ni++ for Me++, then the compound would be called as nickel ferrite, if Fe++ is inserted for Me++, then the compound is ferrous ferrite, written as Fe++ Fe2+++ O4-- or in more familiar form as Fe3 O4.

X-ray crystallography reveals that usually ferrite oxygens have FCC structure with tetrahedral and octahedral interstitial spaces. The tetrahedral space is surrounded by four oxygens and octahedral space is surrounded by six oxygens. These sites are denoted as A-sites and B-sites, respectively. The divalent and trivalent metal ions occupy these spaces. The arrangement of cations in these spaces shows the magnetic properties of these materials.

The magnetization of ferrimagnetic materials can be understood by taking one of the material as an example say, ferrous ferrite [Fe++ Fe2+++ O4--]. This is a natural ferrite called magnetite.

The saturated magnetization of a ferrous ferrite molecule is explained as follows: saturated magnetization can be calculated from the number of unpaired electron spins of the Fe++ and Fe+++ ions. Fe++ ion has six 3d electrons, of which four have unpaired spins and Fe+++ ion has five unpaired electron spins. Assuming all the spins are parallel, we expect a saturated magnetic moment of [4 + 2 × 5] μB = 14 μB per molecule of magnetite. Whereas experimental value is 4.08μB per molecule, so we rule out the parallism of all the electron spins in a molecule. We may conclude that half of the Fe+++ ion electron spins are in one direction and the remaining Fe+++ and Fe++ ion electron spins are in the opposite direction so that the magnetic moment per molecule of ferrous ferrite is 4μB. This is in agreement with the experimental value.

The magnetization in the unit cell of ferrous ferrite is explained in the following way: The unit cell contains 8 molecules of ferrous ferrite or 32 divalent oxygens, 16 trivalent iron ions and 8 divalent iron ions. There are 8 tetrahedral voids called A-sites and 16 octahedral voids called B-sites. In magnetite, 8 Fe+++ ions occupy all the A-sites and the remaining 8 Fe+++ and 8 Fe++ ions occupy B-sites. Figure 7.14 represents the magnetic dipole moments of ferric and ferrous ions in the unit cell. Each arrow represents the magnetic dipole moment of a ion. With this arrangement, the Fe+++ ion contribution to the magnetic moment vanishes completely and the net magnetic moment is due to Fe++ ions only and equal to 4μB per molecule.

 

Figure 7.14 Shows the magnetic dipole moments of ferric and ferrous ions in the unit cell of ferrous ferrite

7.11 Soft and hard magnetic materials

During the process of magnetization, the domain wall moment takes place so that the favourably oriented domains increase in size and unfavourably oriented domains shrink.

Based on the resistance to the moment of domain walls by the applied magnetic field, the area inside the hysteresis loop and on some other properties, the magnetic materials are divided into soft and hard magnetic materials. Now, we shall discuss these materials separately.

(a) Soft magnetic materials

The resistance to the moment of domain walls is less and it is easy to magnetize. The soft magnetic materials are characterized by: (i) low remanent magnetization, (ii) low coercivity, (iii) low hysteresis losses, (iv) high magnetic permeability and (v) high susceptibility so that they can be magnetized and demagnetized easily.

The most widely used soft magnetic materials are: (1) pure iron, (2) alloys of iron-silicon, (3) iron-cobalt, (4) iron-nickel (permalloy) often other alloying elements are added. Some other substances are: (5) mumetal (alloy of Ni, Cu, Cr & Fe) and (6) amorphous ferrous alloys (alloys of Fe, Si & B).

Now, we see the applications of various soft magnetic materials:

  1. pure iron is frequently used as the magnetic core for direct current (DC) applications.
  2. iron-silicon alloys containing up to 5% silica possess high electrical resistivity and high magnetic permeability and are used as core materials for AC current machinery. Eddy current losses could be minimized using iron-silicon alloys. They are used for low-frequency and high-power applications.
  3. Iron-nickel alloys are used for audio frequency applications. In iron-nickel alloys, nickel composition may vary from 35 to nearly 100%. Generally, the permeability increases with an increase of nickel content. Maximum permeability is obtained for 79% of nickel and the rest iron. The alloy containing 79% Ni, 15% Fe, 5% Mo and 0.5% Mn is known as supermalloy that possesses very high permeability.
  4. Iron-cobalt alloys have very high magnetic saturation than either iron or cobalt; maximum saturation is obtained for a composition of about 35 to 50% of cobalt.
  5. Soft magnetic materials are also used in magnetic amplifiers, magnetic switching circuits and the other applications under alternate magnetic fields.

(b) Hard magnetic materials

The resistance to the moment of the magnetic domain walls is large. The causes for such a nature are also due to the presence of impurities of non-magnetic materials or the lattice imperfections. The presence of defects increases the mechanical hardness to the material and an increase the electrical resistivity and reduces eddy current losses. Hard magnetic materials are characterized by: (i) high remanent magnetization, (ii) high coercivity, (iii) high saturation flux density, (iv) low permeability and (v) high hysteresis loss.

Most widely used permanent magnetic materials are low alloy steels containing 0.6% to 1% carbon. Other materials are: (1) alnico [alloy of Al, Ni, Co, Cu and Fe], (2) tungsten steel alloy, (3) platinum-cobalt alloy and (4) invar, etc.

Hard magnetic materials are used to prepare permanent magnets. Most of them are manufactured from alloys of steel with tungsten and chromium. The permanent magnets are used in magnetic separators, magnetic detectors, in speakers used in audio systems and microphones. Hard magnets made of carbon steel find application in the making of magnets for toys and certain types of measuring meters because of its low cost.

Comparison between soft and hard magnetic materials

Soft Magnetic Materials Hard Magnetic Materials
1. Small amount of magnetic field is sufficient to saturately magnetise the material. Since the resistance for the moment of domains is less 1. Large amount of magnetic field is required for saturated magnetization. Since the resistance for the moment of domain is large.
2. Hysteresis loss is less so the area inside the hysteresis loop is less for soft magnetic materials. 2. Hysteresis loss is large so the area inside the hysteresis loop is more for hard magnetic materials.
3. Coercivity and retentivity is less so, the material can be magnetized and demagnetized easily. 3. Coercivity and retentivity is large so, the material can not be easily magnetized and demagnetized.
4. In these materials the magnetic permeability and magnetic susceptibility is large. 4. These materials possess low values of magnetic permeability and magnetic susceptibility.
5. Soft magnetic materials are used in the preparation of magnetic core materials used in transformers, electric motors, magnetic amplifiers, magnetic switching circuits, etc. 5. Hard magnetic materials are used in the preparation of permanent magnets. They are used in loud speakers, toys, in measuring meters, microphones, magnetic detectors, magnetic separators, etc.,

7.12 Applications of ferrites

The various applications are described below:

  1. Ferrites are used in thermal sensing switches used in refrigerators, air conditioners, electronic ovens, etc.
  2. The magnetostrictive property of ferrites is utilized in producing ultrasonic waves from a ferrite rod by the application of an alternating magnetic field.
  3. The insulating property of ferrites finds their use in electric motors; they are also used as flat rings for loud speakers, wind screen wiper motors and correction magnets for TV.
  4. Some ferrites possess high rectangular hysteresis loop, so they are useful in the construction of computer memory system for rapid storage and retrieval of digital information.
  5. Mixed ferrites possess high resistivity and good magnetic properties, so they can be used to prepare cores used in inductors and transformers.
  6. Mn-Zn ferrites are used in television deflection yokes, cores for television line output transformers and standard power supplies. These materials are used in induction cores, antennas for medium and long wave broadcasting, transductors [variable inductors], automatic control systems, frequency modulation, switching, filters, etc.
  7. Ni-Zn ferrites are useful in wide band transformers, antennas for medium and long wave broadcasting, power transformer cores, inductor cores and antennas for short wave broadcasting.
  8. Oxides of γ-Fe2O3, Fe3 O4 and CrO2 are used in magnetic recording of audio, visual and digital information because of their high remanence magnetization. The most widely used material is cobalt modified γ-Fe2O3 and CrO2.
  9. The non-reciprocity of some ferrites, such as garnets, are used in a variety of devices like isolators, calculators, switches, etc. An isolator is a device in which the incident electromagnetic wave can propagate forward, so that there is no reverse wave.

Formulae

  1. μ = μr μoH/m     where     μo = 4π × 10-7H/m
  2. Bo = μoH     and     B = μH so = μr
  3. B = μo (H + M)
  4. M = H [μr – 1]
  5.      for ferromagnetic
  6.      for anti-ferromagnetic
  7.      for para magnetic

Solved Problems

1. The magnetic susceptibility of silicon is –0.4 × 10-5. Calculate the flux density and magnetic moment per unit volume when magnetic field of intensity 5 × 105 A/m is applied.

Sol: Given: X = –0.4 × 10–5

H = 5 × 105 A/m

B = ?  and  M = ?

B = μ0(H + M) = μ0 H(1 + X)

 = 4π × 10-7 × 5 × 105 [1 – 0.4 × 10-5] = 4π × 5 × 10–2 × 0.9996 = 0.62 Wb/m2

M = XH = –0.4 × 10-5 × 5 × 105 = –2.0 A/m.

2. The magnetic field strength in silicon is 1000 A/m. If the magnetic susceptibility is –0.25 × 10–5, calculate the magnetization and flux density in silicon.

Sol: Magnetic field strength (H) = 1000 A/m

Magnetic susceptibility (X) = –0.25 × 10–5

Magnetization (M) = XH = –0.25 × 10–5 × 1000 = –0.25 × 10–2 A/m.

Magnetic flux density (B) = μ0(H + M) = 4π × 10–7 (1000 – 0.25 × 10-2)

 

 

3. When a magnetic material is subjected to a magnetic field of intensity 250 A/m. Its relative permeability is 15. Calculate its magnetization and magnetic flux density.

Sol: Given data are:

Intensity of applied magnetic field (H) = 250 A/m

Relative permeability (μr) = 15

Magnetization (M) = ?

Magnetic flux density (B) = ?

M = H [μr – 1] = 250 [15 – 1] A/m = 250 × 14 = 3500 A/m

B = μ0 [H + M] = 4π × 10–7 [250 + 3500] Wb/m2 = 4.71 × 10-3 Wb/m2

4. Calculate magnetic dipole moment per unit volume and flux density of a material placed in magnetic field of intensity 1000 A/m. The magnetic susceptibility is – 0.42 × 10–3.

Sol: The given data are:

The intensity of magnetic field (H) = 1000 A/m

Magnetic susceptibility (X) = –0.42 × 10–3

Magnetic moment per unit volume or Magnetization (M) = X H

 

 

Flux density or magnetic induction (B) = μ0(H + M)

 

 

5. A circular loop of copper having a diameter of 10 cm carries a current of 500 mA. Calculate the magnetic moment associated with the loop.

 

(Set-2–Nov. 2004), (Set-1–Nov. 2003)

Sol: Magnetic moment, μ = area × current

Diameter of the loop, 2r = 10 cm = 0.1 m

or radius of the loop, r = 5 cm = 0.05 m

Current in the loop, i = 500 mA = 0.5 A

...μ = πr2i = × (0.05)2 × 0.5 = 3.93 × 10–3A – m2

6. A magnetic material has a magnetization of 3300 A/m and flux density of 0.0044 Wb/m2. Calculate the magnetizing force and the relative permeability of the material.

 

(Set-4–Nov. 2003)

Sol: Magnetization, M = 3300 A/m

Flux density, B = 0.0044 Wb/m2

Magnetizing force, H = ?

Relative permeability, μr = ?

B = μ0 [H + M]

 

 

7. An electron in a hydrogen atom circulates with a radius 0.052 nm. Calculate the change in its magnetic moment if a magnetic induction (B) = 3 Wb/m2 acts at right angles to the plane of orbit.

 

(Set-3–Nov. 2004), (Set-2–Nov. 2003)

Sol: Radius of hydrogen atom, r = 0.052 nm = 0.52 × 10–10 m

Magnetic induction that acts perpendicular to orbit, B = 3 Wb/m2

Change in magnetic moment, ∆μ = ?

 

 

8. Calculate the change in magnetic moment of a circulating electron in an applied field of 2 tesla acting perpendicular to the plane of the orbit. Given r = 5.29 × 10-11 m for the radius of the orbit.

 

(Set-3–May 2004)

Sol: Applied magnetic field perpendicular to orbit, B = 2 Tesla

Radius of the orbit, r = 5.29 × 10–11 m

Change in magnetic moment, dμ = ?

 

 

9. A paramagnetic material has 1028 atoms per m3. Its susceptibilty at 350 K is 2.8 × 10 -4. Calculate the susceptibility at 300 K.

 

(Set-4–Nov. 2004)

Sol: Number of atoms, N = 1028/m3

Susceptibility at 350 K, X1 = 2.8 × 10–4

Temperature, T1 = 350 K

Susceptibility at 300 K, X2 = ?

Temperature, T2 = 300 K

For paramagnetic substance

... X1T1 = X2T2

 

 

10. The magnetic field in the interior of a certain solenoid has the value of 6.5 × 10 -4 T when the solenoid is empty. When it is filled with iron, the field becomes 1.4 T. Find the relative permeability of iron.

 

(Set-3–June 2005)

Sol: Magnetic field without iron material, B0 = 6.5 × 10 –4 Tesla

Magnetic field with iron material, B = 1.4 Tesla

The relative permeability of iron,

Multiple Choice Questions

  1. The magnetic susceptibility of a diamagnetic substance is: ( )
    1. negative
    2. zero
    3. positive and low value
    4. positive and high value
  2. Ferrites show: ( )
    1. diamagnetism
    2. paramagnetism
    3. ferromagnetism
    4. ferrimagnetism
  3. A Bohr magneton is equal to: ( )
    1. 9.27 × 10–14 A–m2
    2. 9.27 × 10–24 A–m2
    3. 6.27 × 10–14 A–m2
    4. 6.27 × 10–24 A–m2
  4. If the applied magnetic field will not show any effect on a material, then the material is a: ( )
    1. diamagnetic material
    2. ferromagnetic material
    3. anti-ferromagnetic material
    4. non-magnetic material
  5. A material which magnetizes to a small extent in the opposite direction to the applied external magnetic field is: ( )
    1. ferrimagnetic material
    2. anti-ferromagnetic material
    3. diamagnetic material
    4. paramagnetic material
  6. Examples for diamagnetic materials are: ( )
    1. gold and copper
    2. bismuth and lead
    3. zinc and noble gases
    4. all the above
  7. The materials which are feebly attracted by external magnetic fields are ___________ magnetic materials.()
    1. para
    2. ferro
    3. ferri
    4. anti-ferro
  8. Examples for paramagnetic materials are: ( )
    1. aluminium and platinum
    2. manganese chloride
    3. salts of iron and nickel
    4. all
  9. The magnetic susceptibility is positive and large for___________magnetic materials. ( )
    1. ferro
    2. para
    3. ferri
    4. anti-ferro
  10. The magnetic dipole moments of neighbouring atoms are anti-parallel and unequal for___________magnetic material. ( )
    1. anti-ferro
    2. ferri
    3. dia
    4. para
  11. The domain theory of ferromagnetism was proposed by: ( )
    1. Curie
    2. Ronald
    3. Weiss
    4. Einstein
  12. The polarized light reflected on the surface of a ferromagnetic substance appears as: ( )
    1. non-uniform intensity at different regions on the surface
    2. uniform intensity at different regions on the surface
    3. very low intensity at different regions on the surface
    4. none of the above
  13. If ‘H’ is the intensity of magnetic field in a volume dv, then the field energy in that volume is: ( )
    1. H2 dv
    2. Hdv
    3. Hdv
    4. none
  14. The anisotropy energy in BCC iron along [111] direction over that of [100] direction is: ( )
    1. 105 erg/cm3
    2. 104 erg/cm3
    3. 106 erg/cm3
    4. 103 erg/cm3
  15. If ‘I’ is the current due to the orbital motion of an electron, then the magnetic moment associated with that orbit of area ‘A’ is: ( )
    1. I/A
    2. A/I
    3. I + A
    4. IA
  16. Magnetic dipole moment per unit volume of material is called: ( )
    1. polarization
    2. permeability
    3. magnetization
    4. magnetic induction
  17. Magnetic flux over a unit area of a surface held normal to the flux is: ( )
    1. magnetic induction
    2. magnetic permeability
    3. magnetization
    4. relative magnetic permeability
  18. The neighbouring atomic magnetic moments of anti-ferromagnetic substance is: ( )
    1. equal and parallel
    2. equal and anti-parallel
    3. unequal and parallel
    4. unequal and anti-parallel
  19. The magnetic moment of atom is due to: ( )
    1. the spin of electrons
    2. the angular momentum of the electrons
    3. by the applied magnetic field
    4. all the above
  20. The spin magnetic moments of neighbouring atoms of a ferromagnetic substance are: ( )
    1. parallel
    2. anti-parallel
    3. random
    4. perpendicular
  21. If an electron of mass, me revolving in an orbit with an angular momentum ‘L,’ then it is associated with megnetic moment of: ( )
  22. The SI unit of magnetic moment is: ( )
    1. Wb
    2. Wb/m2
    3. A–m2
    4. A/m2
  23. The magnetostrictive strain energy can be reduced by: ( )
    1. increasing the size of strain-producing horizontal domains
    2. decreasing the size of strain-producing horizontal domains
    3. decreasing the size of strain-producing vertical domains
    4. increasing the size of strain-producing vertical domains
  24. If C and θ are the Curie constant and paramagnetic Curie temperature of a paramagnetic substance at a temperature TK, the magnetic susceptibility is: ( )
    1. none of the above
  25. Soft magnetic materials possess: ( )
    1. low remanent magnetization
    2. low coercivity and hysteresis losses
    3. high magnetic permeability and susceptibility
    4. all the above
  26. Hard magnetic materials possess: ( )
    1. high remanent magnetization and coercivity
    2. low permeability
    3. high hysteresis loss
    4. all the above
  27. Hard magnetic materials are used in: ( )
    1. magnetic separators and detectors
    2. speakers used in audio systems and microphones
    3. in toys and measuring meters
    4. all the above
  28. Ferrites are used in: ( )
    1. thermal-sensing switches used in refrigerators and air conditioners
    2. to produce ultrasonic waves
    3. in electric motors
    4. all the above
  29. The ratio of magnetic flux density in a material to that in vacuum under the same applied magnetic field is called: ( )
    1. relative magnetic permeability
    2. relative permeability
    3. magnetic induction
    4. none of the above
  30. The ratio of magnetization to the applied magnetic field strength of a material is called: ( )
    1. magnetic susceptibility
    2. magnetic permeability
    3. magnetic induction
    4. none of the above
  31. A material which is repelled by an external magnetic field is ___________ magnetic material. ( )
    1. para
    2. ferro
    3. anti-ferro
    4. dia
  32. A material which is strongly attracted by magnetic fields is ___________ magnetic material. ( )
    1. para
    2. ferro
    3. anti-ferro
    4. dia
  33. Examples for ferromagnetic materials are: ( )
    1. iron
    2. cobalt
    3. nickel
    4. all the above
  34. If M stands for a divalent ion, a general formula for ferrites is: ( )
    1. MoFe2 O3
    2. MoFeO3
    3. MoFe2O
    4. MFe2O3
  35. The change in dimensions of a material on magnetization is called: ( )
    1. piezoelectricity
    2. ferroelectricity
    3. magnetostriction
    4. none
  36. Hysteresis means ___________ of an effect behind the cause of effect. ( )
    1. lagging
    2. advancing
    3. both a & b
    4. none
  37. For an anti-ferromagnetic substance, the magnetic susceptibility is maximum at ___________ temperature. ( )
    1. Fermi
    2. Debye
    3. Neel
    4. Curie
  38. The magnetic dipole moment per molecule of ferrous ferrite is equal to: ( )
    1. 2μB
    2. 8μB
    3. 4μB
    4. 16μB
  39. The hysteresis loss is less for ___________ magnetic materials. ( )
    1. dia
    2. para
    3. hard
    4. soft
  40. The alloy containing 79% Ni, 15% Fe, 5% Mo and 0.5% Mn is known as superm alloy possess: ( )
    1. very low permeability
    2. very high permeability
    3. very low magnetic induction
    4. none of the above
  41. ___________ magnetic materials are used in magnetic amplifiers and in magnetic switching circuits. ( )
    1. dia
    2. para
    3. soft
    4. hard
  42. Some ferrites possess rectangular hysteresis loop, so they are used in the construction of ( )
    1. memory
    2. transformer core
    3. permanent magnets
    4. none of the above
  43. Ni–Zn ferrites are used in: ( )
    1. power transformer cores
    2. inductor cores
    3. antenna‘s for short wave broadcasting
    4. all the above
  44. The unit of magnetic permeability of a diamagnetic substance is independent of: ( )
    1. temperature
    2. pressure
    3. humidity
    4. none
  45. The magnetic permeability of a diamagnetic substance is independent of: ( )
    1. temperature
    2. pressure
    3. humidity
    4. none
  46. The ratio of magnetic moment (M) to the angular momentum (L) of an electron is called ___________ ratio. ( )
    1. gyromagnetic ratio
    2. magnetic susceptibility
    3. permeability
    4. none of the above
  47. Below curie temperature, a ferromagnetic substance possess ___________ magnetization. ( )
    1. dia
    2. para
    3. spontaneous
    4. none
  48. The area enclosed by hysteresis loop of a ferromagnetic substance represents ___________ loss per cycle. ( )
    1. magnetization
    2. dielectiric
    3. energy
    4. power
  49. Every domain of a ferromagnetic substance is ___________ magnetized. ( )
    1. dia
    2. spontaneoulsly
    3. para
    4. none
  50. The boundary between domains is called ___________ ( )
    1. Bloch wall
    2. potential wall
    3. both a & b
    4. none
  51. Paramagnetic atoms possess ___________ number of electrons. ( )
    1. even
    2. odd
    3. both a & b
    4. none
  52. A current loop behaves as a ___________ ( )
    1. electric motor
    2. magnetic shell
    3. electric shell
    4. none of the above
  53. Magnetic permeability represents the___________with which a material allows magnetic force of lines to pass through it. ( )
    1. difficult
    2. easy
    3. both a & b
    4. none

Answers

1. a 2. d 3. b
4. d 5. c 6. d
7. a 8. d 9. a
10. b 11. c 12. a
13. a 14. a 15. d
16. c 17. a 18. b
19. d 20. a 21. b
22. c 23. b 24. c
25. d 26. d 27. d
28. d 29. a 30. a
31. d 32. b 33. d
34. a 35. c 36. a
37. c 38. c 39. d
40. b 41. c 42. a
43. d 44. a 45. a
46. a 47. c 48. c
49. b 50. a 51. b
52. b 53. b  

Review Questions

  1. What are paramagnetic and diamagnetic materials? Explain.

     

    (Set-4–Sept. 2006), (Set-1, Set-4–June 2005), (Set-4–Nov. 2004)

  2. Explain the properties of paramagnetic materials.

     

    (Set-3–Nov. 2003)

  3. Define the terms permeability (μ) susceptibility, magnetic induction (B), magnetic field (H) and magnetization (M) with reference to magnetism. Obtain a relation between magnetic susceptibility, magnetization and magnetic field.

     

    (Set-2–Nov. 2004), (Set-1–Nov. 2003)

  4. Explain how the magnetic materials are classified from the atomic point of view.

     

    (Set-4–Nov. 2003)

  5. What are the differences between hard and soft magnetic materials?

     

    (Set-4–Nov. 2003)

  6. Explain the origin of diamagnetism. Obtain an expression for the diamagnetic susceptibility of a magnetic material.

     

    (Set-3–Nov. 2003), (Set-2–Nov. 2003)

  7. Distinguish between ferromagnetic, anti-ferromagnetic and ferrimagnetic materials.

     

    (Set-3–Nov. 2004),

  8. Obtain an expression for paramagnetic susceptibility (X). How does the magnetic susceptibility of a material vary with temperature?

     

    (Set-4–Nov. 2004)

  9. Draw the B-H curve for a ferromagnetic material and identify the retentivity and the coersive field on the curve.

     

    (Set-4–Sept. 2006), (Set-1, Set-4–June 2005)

  10. Explain clearly the differences between hard and soft magnetic materials. What are mixed ferrites? Mention their uses.

     

    (Set-2–June 2005)

  11. How ferrites are superior to ferromagnetic materials?

     

    (Set-2–June 2005)

  12. Give an account of ferromagnetic materials.

     

    (Set-3–May 2004)

  13. Explain the important properties of ferrites.

     

    (Set-2–May 2003), (Set-4–May 2004)

  14. What are the characteristics of soft magnetic materials?

     

    (Set-3–June 2005)

  15. Define magnetization and show that. B = μ0 (H + M).

     

    (Set-3–May 2004)

  16. What is ferromagnetic curie temperature? Discuss the behaviour of a ferromagnetic material below the curie temperature.

     

    (Set-3–June 2005)

  17. In a hydrogen atom, an electron having charge e revolves around the nucleus at a distance of r metre with an angular velocity ‘ω’ rad/sec. Obtain an expression for magnetic moment associated with it due to its orbital motion.

     

    (Set-1–Nov. 2004)

  18. What are the sources of permanent dipole moment in magnetic materials?

     

    (Set-2–Sept. 2008), (Set-4–May 2004), (Set-2–May 2003)

  19. Define the terms magnetic susceptibility, magnetic permeability, magnetic induction and magnetization.

     

    (Set-4–May 2004),(Set-2–May 2003)

  20. Explain hysteresis of a ferromagnetic material.

     

    (Set-1–May 2004), (Set-3–May 2003)

  21. Explain ferrimagnetism and anti-ferromagnetism.

     

    (Set-1–May 2004), (Set-3–May 2003)

  22. How materials are classified as dia or para or ferromagnetism? Explain.

     

    (Set-1–May 2004), (Set-3–May 2003)

  23. What are ferrites? Explain the magnetic properties of ferrites and mention their industrial applications.

     

    (Set-3–May 2007), (Set-2–May 2004), (Set-4–May 2003)

  24. What is ferromagnetism? What are the distinguishing features of ferromagnetism?

     

    (Set-3–May 2007), (Set-2–May 2004), (Set-4–May 2003)

  25. In hydrogen atom, an electron ‘e’ revolves around the nucleus at a distance of ‘r’ metre with an angular velocity ω rad/sec. Obtain an expression for magnetic moment associated with it due to its orbital motion.

     

    (Set-1–May 2003)

  26. Define magnetic moment. Explain the origin of magnetic moment at the atomic level. What is a Bohr magneton?

     

    (Set-1–Nov. 2004), (Set-1–May 2003)

  27. Explain clearly difference between hard and soft magnetic materials.

     

    (Set-4–May 2008)

  28. Explain the hysteresis loop observed in ferromagnetic materials.

     

    (Set-4–May 2008)

  29. Define the terms magnetic susceptibility, magnetic induction and permeability.

     

    (Set-1–May 2006)

  30. How is magnetic susceptibility of a material is measured?

     

    (Set-1–May 2006)

  31. Explain the salient features of anti-ferromagnetic materials.

     

    (Set-1–May 2006)

  32. What is meant by ferromagnetic materials? Give example.

     

    (Set-2–May 2006)

  33. Explain the hysteresis properties of ferromagnetic materials.

     

    (Set-2–May 2006), (Set-2–Sept. 2008)

  34. Mention the various properties of paramagnetic materials.

     

    (Set-2–May 2006)

  35. What are the properties of antiferromagnetic materials?

     

    (Set-1–Sept. 2006)

  36. Explain how antiferromagnetic materials are different from diamagnetic and paramagnetic materials.

     

    (Set-1–Sept. 2006)

  37. State the properties of diamagnetic materials.

     

    (Set-4–Sept. 2007), (Set-2–Sept. 2006)

  38. Explain the terms (i) Magnetic flux density, (ii) Magnetic field strength, (iii) Magnetization and (iv) Magnetic susceptibility. How they are related to each other.

     

    (Set-3–Sept. 2008)

  39. What are hard and soft magnetic materials? Write their characteristic properties and applications.

     

    (Set-3-Sept. 2008)

  40. What is meant by Neel temperature?

     

    (Set-1-Sept. 2006)

  41. Write notes on ferroelectricity.

     

    (Set-2-Sept. 2008)

  42. Draw and explain B-H curve for a ferromegnetic material placed in a magnetic field.

     

    (Set-4-Sept. 2007), (Set-2-Sept. 2006)

  43. Discuss the theory of paramagnetism.

     

    (Set-4-Sept. 2007), (Set-2-Sept. 2006)

  44. Write short notes on hysteresis curve.
  45. Explain ferromagnetism and B–H curve.
  46. Write the importance of hard magnetic materials in engineering applications.
  47. Explain in detail the classification of magnetic materials on the basis of electron spin.
  48. What is Bohr magneton? How is it related to magnetic moment of electron?
  49. Explain in detail domain theory of ferromagnetism.
  50. Explain the origin of magnetic moment. Find the magnetic dipole moments due to orbital and spin motions of an electron.
  51. Show the nature of magnetic dipole moments in ferro, ferri and anti-ferro magnetic materials.
  52. Describe hysteresis loop. How is it used to classify magnets?
  53. Give an account of the uses of ferrites.
  54. Describe the experimental evidence to demonstrate the existence of ferromagnetic domains.
  55. Explain in detail the concept of ferromagnetic domains and explain how it was experimentally established.
  56. What are ferromagnetic domains? Explain their existence.
  57. Explain the different contributions for the formation of domains in a ferromagnetic material.
  58. Write on Bohr magneton.
  59. Write briefly on hysteresis in ferromagnets.
  60. Write the necessary theory to relate electron momentum to the origin of magnetism and write the brief classification of magnetism in materials based on the temperature dependence of susceptibility.
  61. Explain hysteresis in soft and hard magnetic materials and their specific applications.
  62. Explain Weiss theory of ferromagnetic materials.
  63. Give the qualitative explanation of quantum theory for paramagnetic materials.
  64. Explain hysteresis using domain structure.
  65. Explain the properties of ferrimagnetic materials.
  66. Explain ferromagnetism based on domain structure.
  67. Explain the formation of domains based on exchange interaction.
  68. Explain the formation of Bloch wall with a neat diagram.