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Magnetic properties of materials

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Fundamental RelationshipsCoulomb's Law

a force exists between 2 magnetic poles:

where is the force is the permeability of free space, =

, are the magnetic pole strength is the distance separating the poles is the unit radial vector o o o o

unlike gravity, poles come in 2 flavors: + (north-seeking) - (south-seeking) like poles repel (F is +, force is outward) unlike poles attract (F is -, force is inward)

Magnetic Dipole A dipole consists of two poles of opposite polarity and equal strength. The strength of a dipole depends on strength of magnetization of poles and their separation, and is a vector quantity known as dipole moment, which is analogous to mass in gravity: M = ml where M is a vector directed from the negative pole to the positive pole The dipole moment is analogous to mass

Intensity of magnetization Magnetic dipole moment is an extensive quantity. In analogy with gravity, magnetic dipole moment per unit volume is an intensive quantity (like density). This is also called the intensity of magnetization, or I = M/volume = ml/volume = m/area where I and M are vector quantities.M Chaitanya Varma Dept. of Engineering Physics GITAM University

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Permeability Permeability, also called magnetic permeability, is a constant of proportionality that exists between magnetic induction and magnetic field intensity. This constant is equal to approximately 1.257 x 10-6 henry per meter (H/m) in free space (a vacuum). In other materials it can be much different, often substantially greater than the free-space value, which is symbolized o. The permeability factors of some substances change with rising or falling temperature, or with the intensity of the applied magnetic field. Relative permeability, sometimes denoted by the symbol r, is the ratio of the permeability of a specific medium to the permeability of free space. If o represents the permeability of free space (that is, 1.257 x 10-6 H/m) and represents the permeability of the substance in question (also specified in henrys per meter), then the relative permeability, r, is given by: r = / o = (7.958 x 105) Magnetic Induction, B as with gravity, we are interested in force Earth exerts on a unit pole (like acceleration, with g) o or, 'magnetic field intensity' o Analogous to gravitational acceleration (but not acceleration units!) o force per unit pole strength (force exerted on unit magnetic pole)o

(In our analogy with gravity, m here is the Earth's "monopole" field, which is a fiction; Stacey incorrectly calls B "magnetic field, which is H) Magnetic Field Strength, H o if we only had to deal with a vacuum (or even air, since it has negligible magnetic susceptibility), we could always deal with H (magnetic field strength).. o however, in presence of "magnetizable" material, there is a magnetic polarization (or, simply, magnetization) of material which produces an additional field (J) which adds to H o combining the field strength, H, and the magnetic polarization (magnetization), J, is call the magnetic induction, B B = 0H + J J = 0M where 0 = 4 x 10-7 H/m (Henry/meter) is the permeability of free space Units SI system o in SI, for force of 1 Newton and 1 unit pole strength: A/m (H), or Tesla (B) B magnetic induction tesla H Jmagnetic field magnetic polarization, magnetization

T A/m T A/m

amperes per meter tesla amperes per meter

M magnetic dipole moment per unit volume

M Chaitanya Varma Dept. of Engineering Physics GITAM University

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MAGNETIC MOMENTS OF ELECTRONS There are two kinds of electron motion, orbital and spin, and each has a magnetic moment associated with it. The orbital motion of an electron around the nucleus may be likened to a current in a loop of wire having no resistance; both are equivalent to a circulation of charge. The magnetic moment of an electron, due to this motion, may be calculated by an equation

To evaluate m we must know the size and shape of the orbit and the electron velocity. In the original (1913) Bohr theory of the atom, the electron moved with velocity v in a circular orbit of radius r. In cgs units e is the charge on the electron in esu and c the velocity of light, so e/c is the charge in emu. In SI units, the charge of the electron is measured in coulombs. The current, or charge passing a given point per unit time, is then (e=c)(v=2pr) (cgs) or ev/2pr (SI). Therefore,

or An additional postulate of the theory was that the angular momentum of the electron must be an integral multiple of h/2p, where h is Plancks constant. Therefore, mvr=nh/2 where m is the mass of the electron. Combining these relations, we have

for the magnetic moment of the electron in the first (n = 1) Bohr orbit. The spin of the electron was postulated in 1925 in order to explain certain features of the optical spectra of hot gases, particularly gases subjected to a magnetic field (Zeeman effect), and it later found theoretical confirmation in wave mechanics. Spin is a universal property of electrons in all states of matter at all temperatures. The electron behaves as if it were in some sense spinning about its own axis, and associated with this spin are definite amounts of magnetic moment and angular momentum. It is found experimentally and theoretically that the magnetic moment due to electron spin is equal to On the basis of their magnetic properties different materials are classified as: Diamagnetic substance Paramagnetic substance Ferromagnetic substance Diamagnetic Substance Michael Faraday discovered that a specimen of bismuth was repelled by a strong magnet. Diamagnetism occurs in all materials. These materials are those in which individual atoms do not possess any net magnetic moment. [Their orbital and spin magnetic moment add vectorially to become zero]. The atoms of such material however acquire an induced dipole moments when they are placed in an external magnetic field. Some important properties are:M Chaitanya Varma Dept. of Engineering Physics GITAM University

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When suspended in a uniform magnetic field they set their longest axis at right angles to the field as shown

2) In a non-uniform magnetic material, these substances move from stronger parts of the field to the weaker parts. For e.g.,. when diamagnetic liquid is put in a watch glass placed on the two pole pieces of an electromagnet and current is switched on the liquid accumulates on the sides. [Note on increasing the distance between the pole, the effect is reversed] 3) A diamagnetic liquid in a U shaped tube is depressed, when subjected to a magnetic field.

4) The lines of force do not prefer to pass through the specimen, since the ability of a material to permit the passage of magnetic lines of force through it is less.

5) The permeability of the substance, that is, mr < 1. 6) The substance loses its magnetization as soon as the magnetizing field is removed. 7) Such specimen cannot be easily magnetized and so their susceptibility is negative. Example: Bismuth, antimony, copper, gold, quartz, mercury, water, alcohol, air, hydrogen etc. Paramagnetic Substance Paramagnetic substances are attracted by a magnet very feebly. In a sample of a paramagnetic material, the atomic dipole moments initially are randomly oriented in space. When an external field is applied, the dipoles rotate into alignment with field as shown

M Chaitanya Varma Dept. of Engineering Physics GITAM University

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The vector sum of the individual dipole moments is no longer zero. Some important properties are: The paramagnetic substance develops a weak magnetization in the direction of the field. When a paramagnetic rod is suspended freely in a uniform magnetic field, it aligns itself in the direction of magnetic field.

The lines of force prefer to pass through the material rather than air that is mr > 1 that is their permeability is greater than one.

As soon as the magnetizing field is removed the paramagnetics lose their magnetization. In a non-uniform magnetic, the specimen move from weaker parts of the field to the stronger parts (that is it accumulates in the middle). A paramagnetic liquid in U tube placed between two poles of a magnet is elevated.

The magnetization of paramagnetism decreases with increase in temperature. This is because the thermal motion of the atoms tends to disturb the alignment of the dipoles. Example: Aluminum, platinum, chromium, manganese, copper sulphate, oxygen etc., Ferromagnetic Substance Ferromagnetism, like paramagnetism, occurs in materials in which atoms have permanent magnetic dipole moments. The strong interaction between neighboring atomic dipole moments keeps them aligned even when the external magnetic field is removed. Some important properties are: These substances get strongly magnetized in the direction of field. The lines of force prefer to pass through the material rather than air that is mr>1 that is their permeability is greater than one.M Chaitanya Varma Dept. of Engineering Physics GITAM University

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In a non-uniform magnetic, the specimen move from weaker parts of the field to the stronger parts (that is it accumulates in the middle). A paramagnetic liquid in U tube placed between two poles of a magnet is elevated.

For ferromagnetic materials mr is very large and so its susceptibility i.e., Xm is positive.

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