Magnetic susceptibility

In electromagnetism, the magnetic susceptibility (Latin: susceptibilis, “receptive”; denoted $χ$ ) is a measure of how much a material will become magnetized in an applied magnetic field. Mathematically, it is the ratio of magnetization $M$ (magnetic moment per unit volume) to the applied magnetizing field intensity $H$ . This allows a simple classification of most materials’ response to an applied magnetic field into two categories: an alignment with the magnetic field, $χ > 0$ , called paramagnetism, or an alignment against the field, $χ < 0$ , called diamagnetism.

Magnetic susceptibility indicates whether a material is attracted into or repelled out of a magnetic field. Paramagnetic materials align with the applied field and are attracted to regions of greater magnetic field. Diamagnetic materials are anti-aligned and are pushed away, toward regions of lower magnetic fields. On top of the applied field, the magnetization of the material adds its own magnetic field, causing the field lines to concentrate in paramagnetism, or be excluded in diamagnetism.^[1] Quantitative measures of the magnetic susceptibility also provide insights into the structure of materials, providing insight into bonding and energy levels. Furthermore, it is widely used in geology for paleomagnetic studies and structural geology.^[2]

The magnetizability of materials comes from the atomic-level magnetic properties of the particles of which they are made. Usually, this is dominated by the magnetic moments of electrons. Electrons are present in all materials, but without any external magnetic field, the magnetic moments of the electrons are usually either paired up or random so that the overall magnetism is zero (the exception to this usual case is ferromagnetism). The fundamental reasons why the magnetic moments of the electrons line up or do not are very complex and cannot be explained by classical physics (see Bohr–van Leeuwen theorem). However, a useful simplification is to measure the magnetic susceptibility of a material and apply the macroscopic form of Maxwell’s equations. This allows classical physics to make useful predictions while avoiding the underlying quantum mechanical details.

Definition

Volume susceptibility

Magnetic susceptibility is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field. A related term is magnetizability, the proportion between magnetic moment and magnetic flux density.^[3] A closely related parameter is the permeability, which expresses the total magnetization of material and volume.

The volume magnetic susceptibility, represented by the symbol $χ v$ (often simply $χ$ , sometimes $χ m$ – magnetic, to distinguish from the electric susceptibility), is defined in the International System of Units — in other systems there may be additional constants — by the following relationship:^[4]

\mathbf {M} =\chi _{v}\mathbf {H} .

Here

$M$ is the magnetization of the material (the magnetic dipole moment per unit volume), measured in amperes per meter, and
$H$ is the magnetic field strength, also measured in amperes per meter.

$χ v$ is therefore a dimensionless quantity.

Using SI units, the magnetic induction $B$ is related to $H$ by the relationship

\mathbf {B} \ =\ \mu _{0}\left(\mathbf {H} +\mathbf {M} \right)\ =\ \mu _{0}\left(1+\chi _{v}\right)\mathbf {H} \ =\ \mu \mathbf {H}

where $μ 0$ is the vacuum permeability (see table of physical constants), and $(1 + χ v)$ is the relative permeability of the material. Thus the volume magnetic susceptibility $χ v$ and the magnetic permeability $μ$ are related by the following formula:

\mu =\mu _{0}\left(1+\chi _{v}\right).

Sometimes^[5] an auxiliary quantity called intensity of magnetization $I$ (also referred to as magnetic polarisation $J$ ) and measured in teslas, is defined as

\mathbf {I} =\mu _{0}\mathbf {M} .

This allows an alternative description of all magnetization phenomena in terms of the quantities $I$ and $B$ , as opposed to the commonly used $M$ and $H$ .

Mass susceptibility and molar susceptibility

There are two other measures of susceptibility, the mass magnetic susceptibility ( $χ mass$ or $χ g$ , sometimes $χ m$ ), measured in m³/kg (SI) and the molar magnetic susceptibility ( $χ mol$ ) measured in m³/mol that are defined below, where $ρ$ is the density in kg/m³ and $M$ is molar mass in kg/mol:

\chi _{\text{mass}}={\frac {\chi _{v}}{\rho }}

;

\chi _{\text{mol}}=M\chi _{\text{mass}}={\frac {M\chi _{v}}{\rho }}

.

In CGS units

Note that the definitions above are according to SI conventions. However, many tables of magnetic susceptibility give cgs values (more specifically emu-cgs, short for electromagnetic units, or Gaussian-cgs; both are the same in this context). These units rely on a different definition of the permeability of free space:^[6]

\mathbf {B} ^{\text{cgs}}\ =\ \mathbf {H} ^{\text{cgs}}+4\pi \mathbf {M} ^{\text{cgs}}\ =\ \left(1+4\pi \chi _{v}^{\text{cgs}}\right)\mathbf {H} ^{\text{cgs}}

The dimensionless cgs value of volume susceptibility is multiplied by 4 $π$ to give the dimensionless SI volume susceptibility value:^[6]

\chi _{v}^{\text{SI}}=4\pi \chi _{v}^{\text{cgs}}

For example, the cgs volume magnetic susceptibility of water at 20 °C is 7.19×10⁻⁷, which is 9.04×10⁻⁶ using the SI convention.

In physics it is common to see cgs mass susceptibility given in cm³/g or emu/g·Oe⁻¹, so to convert to SI volume susceptibility we use the conversion ^[7]

\chi _{v}^{\text{SI}}=4\pi \,\rho ^{\text{cgs}}\,\chi _{m}^{\text{cgs}}

where $ρ cgs$ is the density given in g/cm³, or

\chi _{v}^{\text{SI}}=\left(4\pi \times 10^{-3}\right)\,\rho ^{\rm {SI}}\,\chi _{m}^{\text{cgs}}

.

The molar susceptibility is measured cm³/mol or emu/mol·Oe⁻¹ in cgs and is converted by considering the molar mass.

Paramagnetism and diamagnetism

If $χ$ is positive, a material can be paramagnetic. In this case, the magnetic field in the material is strengthened by the induced magnetization. Alternatively, if $χ$ is negative, the material is diamagnetic. In this case, the magnetic field in the material is weakened by the induced magnetization. Generally, nonmagnetic materials are said to be para- or diamagnetic because they do not possess permanent magnetization without external magnetic field. Ferromagnetic, ferrimagnetic, or antiferromagnetic materials possess permanent magnetization even without external magnetic field and do not have a well defined zero-field susceptibility.

Experimental measurement

Volume magnetic susceptibility is measured by the force change felt upon a substance when a magnetic field gradient is applied.^[8] Early measurements are made using the Gouy balance where a sample is hung between the poles of an electromagnet. The change in weight when the electromagnet is turned on is proportional to the susceptibility. Today, high-end measurement systems use a superconductive magnet. An alternative is to measure the force change on a strong compact magnet upon insertion of the sample. This system, widely used today, is called the Evans balance.^[9] For liquid samples, the susceptibility can be measured from the dependence of the NMR frequency of the sample on its shape or orientation.^[10]^[11]^[12]^[13]^[14] Another method using NMR techniques measures the magnetic field distortion around a sample immersed in water inside an MR scanner. This method is highly accurate for diamagnetic materials with susceptibilities similar to water.^[15]

Tensor susceptibility

The magnetic susceptibility of most crystals is not a scalar quantity. Magnetic response $M$ is dependent upon the orientation of the sample and can occur in directions other than that of the applied field $H$ . In these cases, volume susceptibility is defined as a tensor

M_{i}=H_{j}\chi _{ij}

where $i$ and $j$ refer to the directions (e.g., $x$ and $y$ in Cartesian coordinates) of the applied field and magnetization, respectively. The tensor is thus rank 2 (second order), dimension (3,3) describing the component of magnetization in the $i$ th direction from the external field applied in the $j$ th direction.

Differential susceptibility

In ferromagnetic crystals, the relationship between $M$ and $H$ is not linear. To accommodate this, a more general definition of differential susceptibility is used

\chi _{ij}^{d}={\frac {\partial M_{i}}{\partial H_{j}}}

where $χ d ij$ is a tensor derived from partial derivatives of components of $M$ with respect to components of $H$ . When the coercivity of the material parallel to an applied field is the smaller of the two, the differential susceptibility is a function of the applied field and self interactions, such as the magnetic anisotropy. When the material is not saturated, the effect will be nonlinear and dependent upon the domain wall configuration of the material.

Several experimental techniques allow for the measurement of the electronic properties of a material. An important effect in metals under strong magnetic fields, is the oscillation of the differential susceptibility as function of $1 / H$ . This behaviour is known as the de Haas–van Alphen effect and relates the period of the susceptibility with the Fermi surface of the material.

In the frequency domain

When the magnetic susceptibility is measured in response to an AC magnetic field (i.e. a magnetic field that varies sinusoidally), this is called AC susceptibility. AC susceptibility (and the closely related “AC permeability”) are complex number quantities, and various phenomena, such as resonance, can be seen in AC susceptibility that cannot in constant-field (DC) susceptibility. In particular, when an AC field is applied perpendicular to the detection direction (called the “transverse susceptibility” regardless of the frequency), the effect has a peak at the ferromagnetic resonance frequency of the material with a given static applied field. Currently, this effect is called the microwave permeability or network ferromagnetic resonance in the literature. These results are sensitive to the domain wall configuration of the material and eddy currents.

In terms of ferromagnetic resonance, the effect of an AC-field applied along the direction of the magnetization is called parallel pumping.

Examples

Magnetic susceptibility of some materials
Material	Temp.	Pressure	Molar susc., $χ mol$		Mass susc., $χ mass$		Volume susc., $χ v$		Molarmass, $M$	Density, $\rho$
Material	(°C)	(atm)	SI (m³/mol)	CGS (cm³/mol)	SI (m³/kg)	CGS (cm³/g)	SI	CGS (emu)	(10⁻³kg/mol = g/mol)	(10³kg/m³ = g/cm³)
Helium^[16]	20	1	−2.38×10⁻¹¹	−1.89×10⁻⁶	−5.93×10⁻⁹	−4.72×10⁻⁷	−9.85×10⁻¹⁰	−7.84×10⁻¹¹	4.0026	1.66×10⁻⁴
Xenon^[16]	20	1	−5.71×10⁻¹⁰	−4.54×10⁻⁵	−4.35×10⁻⁹	−3.46×10⁻⁷	−2.37×10⁻⁸	−1.89×10⁻⁹	131.29	5.46×10⁻³
Oxygen^[16]	20	0.209	+4.3×10⁻⁸	+3.42×10⁻³	+1.34×10⁻⁶	+1.07×10⁻⁴	+3.73×10⁻⁷	+2.97×10⁻⁸	31.99	2.78×10⁻⁴
Nitrogen^[16]	20	0.781	−1.56×10⁻¹⁰	−1.24×10⁻⁵	−5.56×10⁻⁹	−4.43×10⁻⁷	−5.06×10⁻⁹	−4.03×10⁻¹⁰	28.01	9.10×10⁻⁴
Air (NTP)^[17]	20	1					+3.6×10⁻⁷	+2.9×10⁻⁸	28.97	1.29×10⁻³
Water^[18]	20	1	−1.631×10⁻¹⁰	−1.298×10⁻⁵	−9.051×10⁻⁹	−7.203×10⁻⁷	−9.035×10⁻⁶	−7.190×10⁻⁷	18.015	0.9982
Paraffin oil, 220–260cSt^[15]	22	1			−1.01×10⁻⁸	−8.0×10⁻⁷	−8.8×10⁻⁶	−7.0×10⁻⁷		0.878
PMMA^[15]	22	1			−7.61×10⁻⁹	−6.06×10⁻⁷	−9.06×10⁻⁶	−7.21×10⁻⁷		1.190
PVC^[15]	22	1			−7.80×10⁻⁹	−6.21×10⁻⁷	−1.071×10⁻⁵	−8.52×10⁻⁷		1.372
Fused silica glass^[15]	22	1			−5.12×10⁻⁹	−4.07×10⁻⁷	−1.128×10⁻⁵	−8.98×10⁻⁷		2.20
Diamond^[19]	r.t.	1	−7.4×10⁻¹¹	−5.9×10⁻⁶	−6.2×10⁻⁹	−4.9×10⁻⁷	−2.2×10⁻⁵	−1.7×10⁻⁶	12.01	3.513
Graphite^[20] $χ ∥$ (to c-axis)	r.t.	1	−7.5×10⁻¹¹	−6.0×10⁻⁶	−6.3×10⁻⁹	−5.0×10⁻⁷	−1.4×10⁻⁵	−1.1×10⁻⁶	12.01	2.267
Graphite^[20] $χ ∥$	r.t.	1	−3.2×10⁻⁹	−2.6×10⁻⁴	−2.7×10⁻⁷	−2.2×10⁻⁵	−6.1×10⁻⁴	−4.9×10⁻⁵	12.01	2.267
Graphite^[20] $χ ∥$	−173	1	−4.4×10⁻⁹	−3.5×10⁻⁴	−3.6×10⁻⁷	−2.9×10⁻⁵	−8.3×10⁻⁴	−6.6×10⁻⁵	12.01	2.267
Aluminium^[21]		1	+2.2×10⁻¹⁰	+1.7×10⁻⁵	+7.9×10⁻⁹	+6.3×10⁻⁷	+2.2×10⁻⁵	+1.75×10⁻⁶	26.98	2.70
Silver^[22]	961	1					−2.31×10⁻⁵	−1.84×10⁻⁶	107.87
Bismuth^[23]	20	1	−3.55×10⁻⁹	−2.82×10⁻⁴	−1.70×10⁻⁸	−1.35×10⁻⁶	−1.66×10⁻⁴	−1.32×10⁻⁵	208.98	9.78
Copper^[17]	20	1			−1.0785×10⁻⁹		−9.63×10⁻⁶	−7.66×10⁻⁷	63.546	8.92
Nickel^[17]	20	1					600	48	58.69	8.9
Iron^[17]	20	1					200000	15900	55.847	7.874

Sources of confusion in published data

The CRC Handbook of Chemistry and Physics has one of the only published magnetic susceptibility tables. Some of the data (e.g., for aluminium, bismuth, and diamond) is listed as cgs, which has caused confusion to some readers. “cgs” is an abbreviation of centimeters–grams–seconds; it represents the form of the units, but cgs does not specify units. Correct units of magnetic susceptibility in cgs is cm³/mol or cm³/g. Molar susceptibility and mass susceptibility are both listed in the CRC. Some table have listed magnetic susceptibility of diamagnets as positives. It is important to check the header of the table for the correct units and sign of magnetic susceptibility readings.

Application in the geosciences

Magnetism is a useful parameter to describe and analyze rocks. Additionally, the anisotropy of magnetic susceptibility (AMS) within a sample determines parameters as directions of paleocurrents, maturity of paleosol, flow direction of magma injection, tectonic strain, etc.^[2] It is a non-destructive tool, which quantifies the average alignment and orientation of magnetic particles within a sample.^[24]

There are two approaches to measuring paramagnetism that seem to be common. One is to use a balance to measure the slight attraction to a magnet – put sample in a balance, apply magnetic field, look for difference in weight of sample using a Gouy balance or use a torsion balance to observe the attraction in a horizontal plane which takes out the static weight of the sample.

The trouble with these two is the attraction due to paramagnetism is weak compared to the weight of the sample – these are lab bench instruments and the electromagnet consumes a lot of power. Although taking samples of soil is easy enough to bring back to the lab, one really shouldn’t be taking a hammer and chisel to ancient monuments to get a sample for a Gouy balance 😉

It’s not really right to go chiselling a lump off megaliths that have survived thousands of years to insert into a Gouy balance…

The other way of measuring volume magnetic susceptibility is to stick the sample into a coil and measure the inductance – with a different configuration of the coil as a search coil it can be used to measure susceptibility at the rockface.

For a solenoid

L = µ₀µ_rN²A/l

L being the inductance,N the number of turns, A is the cross-sectional area and little l being the length – all of which are constants in any sensor

µ₀ being the permeability of free space, µ₀₌4π×10^-7 N A^-2

µ_r is the effective relative permeability of the sample such that

µ_r= χ_m+1 where

χ_m is the effective magnetic susceptibility of the sample

Bartington Instruments seem to be the go-to guys for magnetic susceptibility instrumentation. From them I learned that one shouldn’t use too high a frequency, which is a bear, My initial prototype ran at 52kHz which is ten to a hundred times too high.

HOW DO YOU MEASURE THE INDUCTANCE OF A COIL?

You resonate it with a capacitance and observe the frequency. It’s easy to measure frequency. The obvious way is that of time immemorial – I used a Colpitts oscillator of grid dip oscillator fame

and measured frequency with a frequency counter via a high impedance scope probe (10M/10pf) on the collector of the transistor. A respectably clean sine wave is to be seen

A roughly 56k sinewave of more than 12V is to be seen at the collector — A roughly 52kHz sinewave of more than 12V is to be seen at the collector

The frequency is not particularly satble long-term - that it's within 0.015% of the frequency just before I measured the sample after an hour is surprising. — The frequency is not particularly stable long-term – that it’s within 0.015% of the frequency just before I measured the sample after an hour is surprising. The first digit is a zero – my camera seems to hate the red LED display of this 30-year old frequency counter

The first thing to note is this is not a big effect – 52,473 Hz unloaded as opposed to 52,441 with the sample. The sensor is a jam jar wound with enamelled wire

From the resonant frequency

f=1/(2π√(LC))

from which I infer the coil was about 0.56mH. Through a whole load of manipulating the formula for inductance

I can derive that if L1 is the inductance of the empty jar and L2 is the inductance of the jar with sample then the effective magnetic susceptibility of the sample χ_m is (L2-L1)/L1, which I then have to divide by 4π to convert from SI to CGS is about 97 µCGS¹ Phil Callahan would not approve…

All volcanic soil & rock is paramagnetic, (from 200 to 2,000 µCGS). According to Dr. Callahan’s research, a soil magnetic susceptibility reading of 0 – 100 µCGS would be poor; 100 – 300 µCGS good; 300 – 800 µCGS very good; & 800 -1200 µCGS above excellent. This force can be added to soil, where it has eroded away, by spreading ground-up paramagnetic rock (basalt, granite, etc.) into the soil.

Philip Callahan from the Pike Agri-Lab website

This generally squares with this chart I pinched from Bartington’s manual for the MS2 susceptibility system–

100 will take you to the granites and metamorphic rocks and 800 gets you about halfway to the left hand side.

There again, my sample takes up less than a quarter of the volume of the solenoid I guess, so if it filled the jar it would creep into very good category. That shows one area that needs thought – filling the sample vessel. A look at Bartington’s susceptibility product range of sensors is instructive – it shows me I want something like the MS2F point probe and maybe a search-coil-like MS2D surface scanning probe eventually. Bartington are good enough to tell me the frequency ranges – the MS2F is 580Hz and the MS2D loop is 958Hz – presumably there are issues of getting the inductance high enough for the loop, hence going up in frequency. Or maybe the higher frequency suits the application better – Bartington seem to know their stuff.

ROOM FOR IMPROVEMENT

there’s over 20V across the tank circuit, so EMC could be an issue[ref]It’s probably not that bad, the wavelength is in the order of 5km so most of the EMC will be due to the near field, it’s not going to propagate that much[/ref]. This will be even less if I go down in frequency
The Q of the tank coil is damped by the circuit – I feel bad about the 470 ohm emitter resistor chucked across half the tapped capacitance which has an impedance of -92j at the operating frequency. I will lose sensitivity and pick up long-term drift because of that, though since this is a differential measurement the latter is not such a big deal.
Form factor – I will usually be taking the sensor to the rock, not the other way round. There’s a sort of assumption that the rock will be bigger than the sensor.
My frequency is way too high I am an order of magnitude off – Bartington use 4.65kHz and 465 Hz in their MS2product, and indicate the lower frequency is more accurate.

The trouble with dropping frequency is that this is looking for a change at the 5 digit level – 1 part in 10,000. That’s two seconds to get a reading at 4.65 kHz (4650/10000) which is okay, but 20s at the lower frequency.

The obvious solution is to either use a frequency multiplier chain before the frequency measurement, or to put a PLL after it with a ÷N counter in the loop. And put a whole load of turns on the coil to get the inductance up

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

Class	χ dependant on B?	Dependant on temperature?	Hysteresis?	Example	χ
Diamagnetic	No	No	No	water	-9.0 ×10^-6
Paramagnetic	No	Yes	No	Aluminium	2.2 ×10^-5
Ferromagnetic	Yes	Yes	Yes	Iron	3000
Antiferromagnetic	Yes	Yes	Yes	Terbium	9.51E-02
Ferrimagnetic	Yes	Yes	Yes	MnZn(Fe₂O₄)₂	2500

Quantity name	permeability alias absolute permeability
Quantity symbol	μ
Unit name	henrys per metre
Unit symbols	H m^-1
Base units	kg m s^-2 A^-2

Quantity	Unit	Formula
Permeability	henrys per metre	μ = L/d
Permittivity	farads per metre	ε = C/d

Quantity name	Relative permeability
Quantity symbol	μ_r
Unit symbols	dimensionless

Material	μ/(H m^-1)	μ_r	Application
Ferrite U 60	1.00E-05	8	UHF chokes
Ferrite M33	9.42E-04	750	Resonant circuit RM cores
Nickel (99% pure)	7.54E-04	600	–
Ferrite N41	3.77E-03	3000	Power circuits
Iron (99.8% pure)	6.28E-03	5000	–
Ferrite T38	1.26E-02	10000	Broadband transformers
Silicon GO steel	5.03E-02	40000	Dynamos, mains transformers
supermalloy	1.26	1000000	Recording heads

Tính chất từ trường của vật liệu (english)

Magnetic susceptibility

Definition

Volume susceptibility

Mass susceptibility and molar susceptibility

In CGS units

Paramagnetism and diamagnetism

Experimental measurement

Tensor susceptibility

Differential susceptibility

In the frequency domain

Examples

Sources of confusion in published data

Application in the geosciences

HOW DO YOU MEASURE THE INDUCTANCE OF A COIL?

ROOM FOR IMPROVEMENT

Magnetic properties of materials

The scope of this page

Magnetization Curves

Diamagnetic and paramagnetic materials

Ferromagnetic materials

Ferrimagnetic materials

Saturation

Materials classification

Permeability

Relative permeability

Variant forms of permeability and related quantities

Initial permeability

Effective permeability

Permeability of a vacuum in the SI

Susceptibility

Mass susceptibility

Terminology for intrinsic fields within materials –

Magnetic moment

Magnetization

Intensity of magnetization

Magnetic polarization

Viết một bình luận Hủy

Table MPS: Magnetic susceptibilities
Material	χ_v / 10^-5
Aluminium	+2.2
Ammonia	-1.06
Bismuth	-16.7
Copper	-0.92
Hydrogen	-0.00022
Oxygen	+0.19
Silicon	-0.37
Water	-0.90

Table MPN: Variant forms of susceptibility
Name	Equation	Symbol	SI Units
bulk susceptibility	M / H	χ, χ_v or κ	dimensionless
mass susceptibility	χ_v / ρ	χ_ρ	m³ kg^-1
molar susceptibility or molar mass susceptibility	χ_v × W_a / ρ	χ_M	m³ mol^-1

Table MPM: Magnetic mass susceptibilities
Material	χ_ρ / (10^-8 m³ kg^-1 )
Aluminium	+0.82
Ammonia	-1.38
Bismuth	-1.70
Copper	-0.107
Hydrogen	-2.49
Oxygen	+133.6
Silicon	-0.16
Water	-0.90

Định lượng	Biểu tượng	Gaussian & css emu ^a	Hệ số chuyển đổi, C ^b	SI & hợp lý mks ^c
Mật độ từ thông, cảm ứng từ	B	gauss (G) ^d	10 ^-4	tesla (T), Wb / m ²
Từ thông	Φ	maxwell (Mx), G ּ cm ²	10 ^-8	weber (Wb), volt giây (V ּ s)
Hiệu điện thế từ, lực từ	U, F	gilbert (Gb)	10/4	ampe (A)
Cường độ từ trường, lực từ hóa	H	oersted (Oe), ^e Gb / cm	10 ³ / 4π	A / m ^f
(Khối lượng) từ hóa ^g	M	emu / cm ^3 h	10 ³	Là
(Khối lượng) từ hóa	4π M	G	10 ³ / 4π	Là
Phân cực từ, cường độ từ hóa	Tôi là tôi	emu / cm ³	4 x x 10 ^-4	T, Wb / m ²ⁱ
(Khối lượng) từ hóa	σ, M	emu / g	1 4π x 10 ^-7	A ּ m ² / kg Wb m / kg
Khoảnh khắc từ	m	emu, erg / G	10 ^-3	A ² m ² , joule mỗi tesla (J / T)
Khoảnh khắc lưỡng cực từ	j	emu, erg / G	4π x 10 ^-10	Wb ּ m ⁱ
(Khối lượng) tính nhạy cảm	χ,	không thứ nguyên, emu / cm ³	4π (4π) ² x 10 ^-7	gà mái không kích thước trên mét (H / m), Wb / (A m)
Tính nhạy cảm (khối lượng)	χ _ρ , k _ρ	cm ³ / g, emu / g	4π x 10 ^-3 (4π) ² x 10 ^-10	m ³ / kgH ּ m ² / kg
(Molar) mẫn cảm	χ _m , κ _mol	cm ³ / mol, emu / mol	4π x 10 ^-6 (4π) ² x 10 ^-13	m ³ / molH ּ m ² / mol
Tính thấm	μ	không thứ nguyên	4 x x 10 ^-7	H / m, Wb / (A m)
Tính thấm tương đối ^j	μ _r	không xác định	–	không thứ nguyên
(Khối lượng) mật độ năng lượng, sản phẩm năng lượng ^k	W	erg / cm ³	10 ^-1	J / m ³
Yếu tố khử từ	D , N	không thứ nguyên	1 / 4π	không thứ nguyên
a . Các đơn vị Gaussian và css emu giống nhau cho các thuộc tính từ tính. Mối quan hệ xác định là B = H + 4π M . b . Nhân một số trong các đơn vị Gaussian với C để chuyển đổi nó thành SI (ví dụ: 1 G x 10 ^-4 T / G = 10 ^-4 T). c . SI ( Système International d’Unitès ) đã được Cục Tiêu chuẩn Quốc gia thông qua. Khi các yếu tố chuyển đổi được đưa ra, yếu tố trên được công nhận theo, hoặc phù hợp với SI và dựa trên định nghĩa B = _o ( H + M ), trong đó μ _o = 4π x 10 ^-7 H / m. Người thấp hơn không được công nhận dưới SI và được dựa trên định nghĩa B = μ _oH + J , nơi biểu tượng Tôi thường được sử dụng ở vị trí của J . d . 1 gauss = 10 ⁵gamma (γ). e . Cả oersted và gauss đều được biểu thị bằng cm ^-1/2 ּ g ^1/2^-1 s ^-1 theo đơn vị cơ sở. f . A / m thường được biểu thị dưới dạng lượt ampere trên mỗi mét khi được sử dụng cho cường độ từ trường. g . Mô men từ tính trên một đơn vị thể tích. h . Tên gọi là emu tinh không phải là một đơn vị. i . Công nhận theo SI, mặc dù dựa trên defition B = μ _oH + J . Xem chú thích c . j . μ _r = μ / μ _o = 1 +, tất cả trong SI. μ _r bằng Gaussian. k . B ּ H và _oM ּ H có đơn vị SI J / m ³ ; M ּ H và B ּ H / 4π có đơn vị Gaussian erg / cm ³ .