Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Magnetic Materials: Units and Terminology, Study notes of Electromagnetic Engineering

In equation 1a, the constant µo is the permeability of free space (4π x 10-7 Hm-1), which is the ratio of B/H measured in a vacuum. In cgs units the ...

Typology: Study notes

2021/2022

Uploaded on 09/12/2022

houhou
houhou 🇺🇸

4

(7)

269 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Magnetic Materials: Units and Terminology
In the study of magnetism there are two systems of units currently in use:
the mks (metres-kilograms-seconds) system, which has been adopted as the S.I. units
the cgs (centimetres-grams-seconds) system, also known as the Gaussian system.
The cgs system is used by many magnets experts due to the numerical equivalence of the magnetic
induction (B) and the applied field (H).
When a field is applied to a material it responds by producing a magnetic field, the magnetisation
(M). This magnetisation is a measure of the magnetic moment per unit volume of material, but can
also be expressed per unit mass, the specific magnetisation (σ). The field that is applied to the
material is called the applied field (H) and is the total field that would be present if the field were
applied to a vacuum. Another important parameter is the magnetic induction (B), which is the total
flux of magnetic field lines through a unit cross sectional area of the material, considering both lines
of force from the applied field and from the magnetisation of the material. B, H and M are related by
equation 1a in S.I. units and by equation 1b in cgs units.
B = µo (H + M)
Equ.1a
B = H + 4 π M
Equ.1b
In equation 1a, the constant µo is the permeability of free space (4π x 10-7 Hm-1), which is the ratio
of B/H measured in a vacuum. In cgs units the permeability of free space is unity and so does not
appear in equation 1b. The units of B, H and M for both S.I. and cgs systems are given in table 2.
Note that in the cgs system 4πM is usually quoted as it has units of Gauss and is numerically
equivalent to B and H.
Another equation to consider at this stage is that concerning the magnetic susceptibility (x),
equation 2, this is the same for S.I. and cgs units. The magnetic susceptibility is a parameter that
demonstrates the type of magnetic material and the strength of that type of magnetic effect.
Equ.2
Sometimes the mass susceptibility (χ
m
) is quoted and this has the units of m
3
kg
-1
and can be
calculated by dividing the susceptibility of the material by the density.
Another parameter that demonstrates the type of magnetic material and the strength of that type of
magnetic effect is the permeability (µ) of a material, this is defined in equation 3 (the same for S.I.
and cgs units).
Equ.3
In the S.I. system of units, the permeability is related to the susceptibility, as shown in equation 4
and can also be broken down into µ
0
and the relative permeability (µ
r
), as shown in equation 5.
pf2

Partial preview of the text

Download Magnetic Materials: Units and Terminology and more Study notes Electromagnetic Engineering in PDF only on Docsity!

Magnetic Materials: Units and Terminology

In the study of magnetism there are two systems of units currently in use:

  • the mks (metres-kilograms-seconds) system, which has been adopted as the S.I. units
  • the cgs (centimetres-grams-seconds) system, also known as the Gaussian system.

The cgs system is used by many magnets experts due to the numerical equivalence of the magnetic

induction (B) and the applied field (H).

When a field is applied to a material it responds by producing a magnetic field, the magnetisation

(M). This magnetisation is a measure of the magnetic moment per unit volume of material, but can

also be expressed per unit mass, the specific magnetisation (σ). The field that is applied to the

material is called the applied field (H) and is the total field that would be present if the field were

applied to a vacuum. Another important parameter is the magnetic induction (B), which is the total

flux of magnetic field lines through a unit cross sectional area of the material, considering both lines

of force from the applied field and from the magnetisation of the material. B, H and M are related by

equation 1a in S.I. units and by equation 1b in cgs units.

B = μo (H + M) Equ.1a B = H + 4 π M Equ.1b

In equation 1a, the constant μo is the permeability of free space (4π x 10-7 Hm-1), which is the ratio

of B/H measured in a vacuum. In cgs units the permeability of free space is unity and so does not

appear in equation 1b. The units of B, H and M for both S.I. and cgs systems are given in table 2.

Note that in the cgs system 4πM is usually quoted as it has units of Gauss and is numerically

equivalent to B and H.

Another equation to consider at this stage is that concerning the magnetic susceptibility (x),

equation 2, this is the same for S.I. and cgs units. The magnetic susceptibility is a parameter that

demonstrates the type of magnetic material and the strength of that type of magnetic effect.

Equ.

Sometimes the mass susceptibility (χm) is quoted and this has the units of m^3 kg-1^ and can be

calculated by dividing the susceptibility of the material by the density.

Another parameter that demonstrates the type of magnetic material and the strength of that type of

magnetic effect is the permeability (μ) of a material, this is defined in equation 3 (the same for S.I.

and cgs units).

Equ.

In the S.I. system of units, the permeability is related to the susceptibility, as shown in equation 4

and can also be broken down into μ 0 and the relative permeability (μr), as shown in equation 5.

μr = χ + 1 Equ. μ = μo μr Equ.

Finally, an important parameter (in S.I. units) to know is the magnetic polarisation (J), also referred

to as the intensity of magnetisation (I). This value is effectively the magnetisation of a sample

expressed in Tesla, and can be calculated as shown in equation 6.

J = μo M Equ. Quantity Gaussian (cgs units) S.I. Units Conversion Factor (cgs to S.I.) Magnetic Induction (B) G T 10 - Applied Field (H) Oe A m-1^103 / 4π Magnetisation (M) -- A m-1^103 Magnetisation (4πM) G -- 103 Magnetic Polarisation (J) -- T -- Specific Magnetisation (σ) emu g-1^ J T kg-1^1 Permeability (μ) Dimensionless H m-1^4 π 10 - Relative Permeability (μr) -- Dimensionless -- Susceptibility (χ) Emu cm-3^ Oe-1^ Dimensionless 4 π Maximum Energy Product (BHmax) M G Oe K J m-3^102 / 4π Table 1: The relationship between some magnetic parameters in cgs and S.I. units. (Where: G = Gauss, Oe = Oersted, T = Tesla)