Chapter 2 Brief review of magnetism and relevant effects
2.1 Magnetism
The first writings of magnetism appeared with a kind of mineral called magnetite (Fe3O4
The discovery of two regions named magnetic poles, or sometimes just
“poles,” which attracted a piece of iron more strongly than the rest of the magnetite, this discovery was made by P. Peregrines about 1269 A.D.
Sometime later, Coulomb (1736-1806) found that there were two types of poles, now called positive or north poles, and negative or south poles. There is always with magnets and felt the mysterious forces of attraction and repulsion between two magnetic poles[3, 16]. The mysterious forces of attraction and repulsion between the two magnetic poles can be felt. This force of attraction and repulsion is proportional to the product of the strength of the poles and inversely proportional to square of the distance between them. This is Coulomb’s law, which can be written mathematically as,
), which has been claimed that the Chinese used it in compasses sometime before 2500 B.C., but the precise date still remained unknown[3, 16].
𝐹⃑ = 𝑘𝑝1𝑝2
𝑟2 𝑟⃑0 (2.1)
10
where 𝐹⃑ is the force, p1 and p2
When a magnetic pole creates a magnetic field around it, and this field will then produces a force on second pole nearby. Experiment shows that this force is directly proportional to the product of the pole strength and field strength or field strength or field intensity 𝐻��⃑,
the pole strengths, r the distance between the poles, and 𝑟⃑0 one unit vector directed along r. The constant of proportionality
k that occurs permits a definition of pole strength, and the proportionality
constant k is equal 1 in the cgs-emu unit.𝐹⃑ = 𝑘𝑝𝐻��⃑. (2.2)
The equation 2.2 then defines 𝐻��⃑, a field of unit strength is one which exerts a force 1 dyne on a unit pole. A field of unit strength has an intensity of one oersted (Oe).
Besides, a magnet with poles of strength p located near each end and separated by distance l. Suppose the magnet is placed at an angle
θ
to a11
where m is the magnetic moment of the magnet. It is the moment of torque exerted on the magnet when it is at right angles to a uniform field of 1 Oe[2, 3, 16].
Consider a piece of iron is subjected to a magnetic field, it becomes magnetized, and the level of its magnetism depends on the strength of the field.
We therefore need a quantity to describe the degree to which a body is magnetized. The application of an external magnetic field causes both an alignment of the magnetic moments of the spinning electrons and an induced magnetic moment due to a change in the orbital motion of electrons In order to obtain a formula for determining the quantitative change in the magnetic flux density caused by the presence of a magnetic material, we let 𝑚��⃑𝑘 Rbe the magnetic moment of an atom. If there are n atoms per unit volume, we define a magnetization vector, 𝑀��⃑, as
𝑀��⃑ = lim∆𝑣→0∑𝑛∆𝑣𝑘=1𝑚��⃑𝑘
∆𝑣 (2.5)
Where ∆ν is the volume and n is the number of ∆ν[2, 16].
The magnetic properties of a material are characterized not only by the magnitude and sign of 𝑀��⃑ but also by the way in which 𝑀��⃑ varies with 𝐻��⃑.
The scalar ratio of these two quantities is called the susceptibility
χ
:𝜒 =𝑀
𝐻 (2.6)
12
Now they can be roughly classified into three main groups in accordance with their
χ
values[3, 16, 17].(1) Diamagnetic, if
χ
is a very small negative number.Electrons which constitute a close shell in an atom usually have their spin and orbital moments oriented so that the atom as a whole has no net moment.
Thus the monoatomic rare gases He, Ne, Ar, etc., which have closed-shell electronic structures, are all diamagnetic. The macroscopic effect of this is equivalent to that of a negative magnetization that can be described by a negative magnetic susceptibility. The effect is usually very small, and
χ
for most known diamagnetic materials is in the order of -10-5(2) Paramagnetic, if
χ
is a very small positive number.Arises mainly from the magnetic dipole moments of the spinning electrons.
The alignment forces, acting upon molecular dipoles by the applied field, are counteracted by the deranging effects of thermal agitation. Unlike diamagnetism, which is essentially independent of temperature, the paramagnetic effect is temperature dependent, being stronger at lower temperatures where there is less thermal collision. (i.e., Na, Al)
. (i.e., Cu, Hg, Ag)
(3) Ferromagnetic, if
χ
is a large positive number.The magnetization of ferromagnetic materials can be many orders of magnitude larger than that of paramagnetic substances. Ferromagnetism can be explained in terms of magnetized domains. I will show more detail in the next section.
13
Besides, engineers are usually concerned only with ferromagnetic materials and need to know the total flux density 𝐵�⃑ produced by a given field, then engineers become the definition in mks system. In addition, engineers are usually only concerned with ferromagnetic materials and the total flux density 𝐵�⃑
produced by a given field. The mks system is generally used as the unit system in engineering application. They often find the 𝐵�⃑, 𝐻��⃑ curve, also called a magnetization curve, more useful than the 𝑀��⃑, 𝐻��⃑ curve. The ratio of B to H is called the permeability
µ
:𝜇 = 𝐵
𝐻 ( 𝐻
𝑚 , 𝑖𝑛 𝑚𝑘𝑠 𝑠𝑦𝑠𝑡𝑒𝑚) (2.7)
When the magnetic properties of the medium are linear and isotropic, the magnetization is directly proportional to the magnetic field intensity:
𝐵�⃑ = 𝜇𝐻��⃑ is the permeability of free space is chosen to be
Where the proportionality constant k is equal to 4π/µ0 in the mks system in
14
equation (2.1)
Fig. 2.1 Bar magnet in a uniform field[3].
15