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# Electromagnetic unit conversion (conversion between SI system and CGS system)

There are three basic physical quantities H (magnetic field), m (magnetization) and B (magnetic induction) in the magnetic field. In the international system of units (SI), the units are a / m, a / M and T; in the Gauss system of units (CGS), they are OE, EMU / cm3 (or GS), GS, and EMU can also be used as the unit. In the following add subscript addition and distinction, such as EMU (H), EMU (m), EMU (b).

Friends who come into contact with magnetic materials often encounter a variety of electrical units or magnetic units. In addition to the general international system units, the Gauss system units are also used in electromagnetics, which makes us feel that the units of electromagnetism are very complex. For example, the intrinsic coercivity Hcj has different description methods under the two unit systems. 960ka / m under SI system is 12koe under CGS system. Today, I will take you to summarize the units in electromagnetism and the conversion relationship between different unit systems.

## What is the unit system?

All kinds of physical quantities are related to each other through the equations describing the laws of nature and the equations defining new physical quantities. In order to formulate the unit system and introduce the concept of dimension, a group of independent physical quantities and their units are usually selected as the basic physical quantities and basic units, and then the scale constants are selected according to a series of specific physical formulas to determine the dimensions and units of other physical quantities (derived quantities). The dimension of the derived quantity is expressed by the power of the basic physical quantity, and the derived unit is expressed by the basic unit. Some derived units have special names and symbols. Thus, the units of various physical quantities form an organic and regular whole, which is the physical unit system.
The best advantage of skillfully using different unit systems to express formulas is that it can greatly simplify formulas and reduce some complex constants to 1, which is conducive to our derivation and understanding. This is why there are multiple unit systems in the field of electromagnetics.

## International system (SI system) and Gauss system (CGS system)

The unit system of electromagnetics in the international system of units is the MKSA rational system. MKSA stipulates the units of four basic physical quantities in electromagnetics, that is, the units of length, mass, time and current intensity are respectively meter (m), kilogram (kg), second (s) and Ampere (a).
Gauss unit system is established on the basis of absolute electrostatic unit system (CGSE unit system or e.s.u) and absolute electromagnetic unit system (CGSM unit system or e.m.u) of electromagnetics. Gauss unit system is a unified unit system of electromagnetics, which is also called mixed unit system. In absolute electrostatic unit system, length, mass and time are selected as basic quantities, and their units are centimeter (CM), gram (g) and second (s).

The conversion relations of these quantities are as follows:

 SI CGS Conversion B T Gs or emu(B) 1T=104Gs M A/m emu(M) or Gs※ H A/m Oe or emu(H)

※ The unit of magnetization GS and the unit of magnetic induction gs are different under the Gauss system, B = H + 4P m, they differ by a coefficient of 4 π. The units of several basic quantities in the Gauss system are: time s, length cm, mass g, current ESU (I) (in the Gauss system, the current is measured by the electrostatic unit system CGSE), and the conversion relationship is 1A = 3´109 esu(I ).

In addition, the unit conversion formula of magnetic moment and magnetization (the magnetic field unit is measured by the magnetostatic unit system) is as follows:

Note: there are two kinds of current units mentioned above. Under Gauss system, the current is measured by CGSE unit system; however, when deriving magnetic quantities, the magnetostatic unit system is used.
The following is a detailed introduction to the measurement of international system of units, electrostatic system of units and magnetostatic system of units.

## Mechanical dimensions and units

The laws of mechanical physics have the same form in the international system of units (SI) and Gauss system of units (CGS), and they all take length, time and mass as the basic dimensions, so all mechanical quantities have the same dimensions.
Table 1 Mechanical Dimensions and units

 Physical quantity Dimension International unit Gauss unit Conversion relationship Length L m cm 1 m = 100 cm Time T s s Frequency T –1 Hz Hz Quality M kg g 1 kg = 1000 g Power M LT 2 N dyn 1N = 105 dyn Energy L2 *T –2 * M J erg 1J = 107 erg Rate of work L2 *T –3 * M W erg/s 1W = 107 erg / s

## Electrostatic dimensions and units

Gauss system has two sets of unit systems in electromagnetism. One is based on Coulomb’s law, which is called electrostatic system, denoted as CGSE, and the other is based on Ampere’s law, which is called magnetostatic system, denoted as CGSM.

Physical quantity International System Electrostatics Magnetostatic system
Dimension Unit Dimension Unit Dimension Unit
L T M I L T M L T M
Charge 0 1 0 1 C
 3/2
-1
 1/2
esu(I)
 1/2
0
 1/2
emu(I)
Electric current 0 0 0 1 A
 3/2
-2
 1/2
esu(A)
 1/2
-1
 1/2
emu(A)
Potential 2 -3 1 -1 V
 1/2
-1
 1/2
esu(V)
 3/2
-2
 1/2
emu(V)
Resistance 2 -3 1 -2 Ω -1 1 0 s/cm 1 -1 0 cm/s
Capacitance -2 4 -1 2 F 1 0 0 cm -1 2 0 s2/cm
Inductance 2 -2 1 -2 H -1 2 0 s2/cm 1 0 0 cm
Magnetic intensity 0 -2 1 -1 T 3 0
 1
1 -1
 1
G
Magnetic flux 2 -2 1 -1 Wb
 2
0
 2
 2
-1
 2
G*cm2
Resistivity 3 -3 1 -2 Ω.m 0 1 0 s 2 -1 0 cm 2s-1

Table.3 conversion of some basic electromagnetic units

 Physical quantity International System Electrostatics Magnetostatic system Charge 1C 2.99792458*10^9 esu(I) Electric current 1A 2.99792458*10^9 esu(A) Potential 1V 3.33564096*10^(-3) esu(V) Resistance 1Ω (8.98755179*10^11)^(-1) (cm/s)^(-1) Capacitance 1F 8.98755179*10^11 cm Inductance 1H 1.11265005*10^(-12) (cm/s2)^(-1) Magnetic induction 1T 104 Magnetic flux 1Wb 108 Magnetic field intensity 1A/m 4p *10-3 Oe Magnetization 1A/m 10-3 esu(M)
Source: China Permanent Magnet Manufacturer – www.rizinia.com