`color{blue} ✍️`The discussion in the previous section helps us to classify materials as diamagnetic, paramagnetic or ferromagnetic. In terms of the susceptibility `color{blue}(χ)` , a material is diamagnetic if `color{blue}(χ)` is negative, para- if `color{blue}(χ)` is positive and small, and ferro- if `color{blue}(χ)` is large and positive.
`color {blue}{➢➢}`A glance at Table 5.3 gives one a better feeling for these materials. Here ε is a small positive number introduced to quantify paramagnetic materials. Next, we describe these materials in some detail.
`color{green}bbul("Diamagnetism")`
`color {blue}{➢➢}`Diamagnetic substances are those which have tendency to move from stronger to the weaker part of the external magnetic field. In other words, unlike the way a magnet attracts metals like iron, it would repel a diamagnetic substance.
`color {blue}{➢➢}`Figure 5.12(a) shows a bar of diamagnetic material placed in an external magnetic field. The field lines are repelled or expelled and the field inside the material is reduced. In most cases, as is evident from Table 5.2, this reduction is slight, being one part in `color{blue}(10^5)`. When placed in a non-uniform magnetic field, the bar will tend to move from high to low field.
`color {blue}{➢➢}`The simplest explanation for diamagnetism is as follows. Electrons in an atom orbiting around nucleus possess orbital angular momentum. These orbiting electrons are equivalent to current-carrying loop and thus possess orbital magnetic moment. Diamagnetic substances are the ones in which resultant magnetic moment in an atom is zero.
`color {blue}{➢➢}`When magnetic field is applied, those electrons having orbital magnetic moment in the same direction slow down and those in the opposite direction speed up. This happens due to induced current in accordance with Lenz’s law which you will study in Chapter 6.
`color {blue}{➢➢}`Thus, the substance develops a net magnetic moment in direction opposite to that of the applied field and hence repulsion.
`color {blue}{➢➢}`Some diamagnetic materials are bismuth, copper, lead, silicon, nitrogen (at STP), water and sodium chloride. Diamagnetism is present in all the substances. However, the effect is so weak in most cases that it gets shifted by other effects like paramagnetism, ferromagnetism, etc.
`color {blue}{➢➢}`The most exotic diamagnetic materials are superconductors. These are metals, cooled to very low temperatures which exhibits both perfect conductivity and perfect diamagnetism.
`color {blue}{➢➢}` Here the field lines are completely expelled! `color{blue}(χ = –1)` and `color{blue}(μ_r = 0)` A superconductor repels a magnet and (by Newton’s third law) is repelled by the magnet. The phenomenon of perfect diamagnetism in superconductors is called the Meissner effect, after the name of its discoverer.
`color {blue}{➢➢}`Superconducting magnets can be gainfully exploited in variety of situations, for example, for running magnetically levitated superfast trains. 5.6.2 Paramagnetism
`color{green}bbul("Paramagnetism")`
`color {blue}{➢➢}`Paramagnetic substances are those which get weakly magnetised when placed in an external magnetic field. They have tendency to move from a region of weak magnetic field to strong magnetic field, i.e., they get weakly attracted to a magnet.
`color {blue}{➢➢}`The individual atoms (or ions or molecules) of a paramagnetic material possess a permanent magnetic dipole moment of their own. On account of the ceaseless random thermal motion of the atoms, no net magnetisation is seen.
`color{blue} ✍️`In the presence of an external field `color{blue}(B_0)`, which is strong enough, and at low temperatures, the individual atomic dipole moment can be made to align and point in the same direction as `color{blue}(B_0).` Figure 5.12(b) shows a bar of paramagnetic material placed in an external field.
`color {blue}{➢➢}`The field lines gets concentrated inside the material, and the field inside is enhanced. In most cases, as is evident from Table 5.2, this enhancement is slight, being one part in `color{blue}(10^5)`.
`color {blue}{➢➢}`When placed in a non-uniform magnetic field, the bar will tend to move from weak field to strong. Some paramagnetic materials are aluminium, sodium, calcium, oxygen (at STP) and copper chloride. Experimentally, one finds that the magnetisation of a paramagnetic material is inversely proportional to the absolute temperature `color{blue}(T)`,
`color{blue}(M = C(B_0)/T)`
......................[5.20 (a)]
`color {blue}{➢➢}`or equivalently, using Eqs. (5.12) and (5.17)
`color{blue}(χ= C(mu_0)/T)`
.......................... [5.20 (b)]
`color {blue}{➢➢}`This is known as Curie’s law, after its discoverer Pieree Curie (1859- 1906). The constant `color{blue}(C)` is called Curie’s constant. Thus, for a paramagnetic material both `color{blue}(χ)` and `color{blue}(μ_r)` depend not only on the material, but also (in a simple fashion) on the sample temperature. As the field is increased or the temperature is lowered, the magnetisation increases until it reaches the saturation value Ms, at which point all the dipoles are perfectly aligned with the field. Beyond this, Curie’s law [Eq. (5.20)] is no longer valid.
`color{blue} ✍️`The discussion in the previous section helps us to classify materials as diamagnetic, paramagnetic or ferromagnetic. In terms of the susceptibility `color{blue}(χ)` , a material is diamagnetic if `color{blue}(χ)` is negative, para- if `color{blue}(χ)` is positive and small, and ferro- if `color{blue}(χ)` is large and positive.
`color {blue}{➢➢}`A glance at Table 5.3 gives one a better feeling for these materials. Here ε is a small positive number introduced to quantify paramagnetic materials. Next, we describe these materials in some detail.
`color{green}bbul("Diamagnetism")`
`color {blue}{➢➢}`Diamagnetic substances are those which have tendency to move from stronger to the weaker part of the external magnetic field. In other words, unlike the way a magnet attracts metals like iron, it would repel a diamagnetic substance.
`color {blue}{➢➢}`Figure 5.12(a) shows a bar of diamagnetic material placed in an external magnetic field. The field lines are repelled or expelled and the field inside the material is reduced. In most cases, as is evident from Table 5.2, this reduction is slight, being one part in `color{blue}(10^5)`. When placed in a non-uniform magnetic field, the bar will tend to move from high to low field.
`color {blue}{➢➢}`The simplest explanation for diamagnetism is as follows. Electrons in an atom orbiting around nucleus possess orbital angular momentum. These orbiting electrons are equivalent to current-carrying loop and thus possess orbital magnetic moment. Diamagnetic substances are the ones in which resultant magnetic moment in an atom is zero.
`color {blue}{➢➢}`When magnetic field is applied, those electrons having orbital magnetic moment in the same direction slow down and those in the opposite direction speed up. This happens due to induced current in accordance with Lenz’s law which you will study in Chapter 6.
`color {blue}{➢➢}`Thus, the substance develops a net magnetic moment in direction opposite to that of the applied field and hence repulsion.
`color {blue}{➢➢}`Some diamagnetic materials are bismuth, copper, lead, silicon, nitrogen (at STP), water and sodium chloride. Diamagnetism is present in all the substances. However, the effect is so weak in most cases that it gets shifted by other effects like paramagnetism, ferromagnetism, etc.
`color {blue}{➢➢}`The most exotic diamagnetic materials are superconductors. These are metals, cooled to very low temperatures which exhibits both perfect conductivity and perfect diamagnetism.
`color {blue}{➢➢}` Here the field lines are completely expelled! `color{blue}(χ = –1)` and `color{blue}(μ_r = 0)` A superconductor repels a magnet and (by Newton’s third law) is repelled by the magnet. The phenomenon of perfect diamagnetism in superconductors is called the Meissner effect, after the name of its discoverer.
`color {blue}{➢➢}`Superconducting magnets can be gainfully exploited in variety of situations, for example, for running magnetically levitated superfast trains. 5.6.2 Paramagnetism
`color{green}bbul("Paramagnetism")`
`color {blue}{➢➢}`Paramagnetic substances are those which get weakly magnetised when placed in an external magnetic field. They have tendency to move from a region of weak magnetic field to strong magnetic field, i.e., they get weakly attracted to a magnet.
`color {blue}{➢➢}`The individual atoms (or ions or molecules) of a paramagnetic material possess a permanent magnetic dipole moment of their own. On account of the ceaseless random thermal motion of the atoms, no net magnetisation is seen.
`color{blue} ✍️`In the presence of an external field `color{blue}(B_0)`, which is strong enough, and at low temperatures, the individual atomic dipole moment can be made to align and point in the same direction as `color{blue}(B_0).` Figure 5.12(b) shows a bar of paramagnetic material placed in an external field.
`color {blue}{➢➢}`The field lines gets concentrated inside the material, and the field inside is enhanced. In most cases, as is evident from Table 5.2, this enhancement is slight, being one part in `color{blue}(10^5)`.
`color {blue}{➢➢}`When placed in a non-uniform magnetic field, the bar will tend to move from weak field to strong. Some paramagnetic materials are aluminium, sodium, calcium, oxygen (at STP) and copper chloride. Experimentally, one finds that the magnetisation of a paramagnetic material is inversely proportional to the absolute temperature `color{blue}(T)`,
`color{blue}(M = C(B_0)/T)`
......................[5.20 (a)]
`color {blue}{➢➢}`or equivalently, using Eqs. (5.12) and (5.17)
`color{blue}(χ= C(mu_0)/T)`
.......................... [5.20 (b)]
`color {blue}{➢➢}`This is known as Curie’s law, after its discoverer Pieree Curie (1859- 1906). The constant `color{blue}(C)` is called Curie’s constant. Thus, for a paramagnetic material both `color{blue}(χ)` and `color{blue}(μ_r)` depend not only on the material, but also (in a simple fashion) on the sample temperature. As the field is increased or the temperature is lowered, the magnetisation increases until it reaches the saturation value Ms, at which point all the dipoles are perfectly aligned with the field. Beyond this, Curie’s law [Eq. (5.20)] is no longer valid.