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oersted
Unit systemGaussian units
Unit ofmagnetic field strength
SymbolOe
Named afterHans Christian Ørsted
Derivation1 dyn/Mx
Conversions
1 Oe in ...... is equal to ...
   Gaussian base units   1 cm−1/2⋅g1/2⋅s−1
   SI units   (4π)−1×103 A/m ≈ 79.57747 A/m

The oersted (/ˈɜːrstɛd/,[1] symbol Oe) is the coherent derived unit of the auxiliary magnetic field H in the CGS-EMU and Gaussian systems of units.[2] It is equivalent to 1 dyne per maxwell.

Difference between Gaussian and SI systems

[edit]

In the Gaussian system, the unit of the H-field is the oersted and the unit of the B-field is the gauss. In the SI, the unit ampere per metre (A/m), which is equivalent to newton per weber, is used for the H-field and the unit tesla is used for the B-field.[3]

History

[edit]

The unit was established by the IEC in the 1930s[4] in honour of Danish physicist Hans Christian Ørsted. Ørsted discovered the connection between magnetism and electric current when a magnetic field produced by a current-carrying copper bar deflected a magnetised needle during a lecture demonstration.[5]

Definition

[edit]
Cassette tape label with coercivity (a measure of the external magnetic flux required to magnetize the tape) measured in oersteds

The oersted is defined as a dyne per unit pole.[clarification needed][6] The oersted corresponds to ⁠1000/4π⁠ (≈79.5775) amperes per metre, in terms of SI units.[7][8][9][10]

The H-field strength inside a long solenoid wound with 79.58 turns per metre of a wire carrying 1 A is approximately 1 oersted. The preceding statement is exactly correct if the solenoid considered is infinite in length with the current evenly distributed over its surface.

The oersted is closely related to the gauss (G), the CGS unit of magnetic flux density. In vacuum, if the magnetizing field strength is 1 Oe, then the magnetic field density is 1 G, whereas in a medium having permeability μr (relative to permeability of vacuum), their relation is

Because oersteds are used to measure magnetizing field strength, they are also related to the magnetomotive force (mmf) of current in a single-winding wire-loop:[11]

Stored energy

[edit]
Main article: maximum energy product

The stored energy in a magnet, called magnet performance or maximum energy product[12] (often abbreviated BHmax), is typically measured in units of megagauss-oersteds (MG⋅Oe).

See also

[edit]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Oersted

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from Grokipedia
The oersted (symbol Oe) is the centimetre–gram–second system (CGS) unit of magnetic field strength (H). It is named after the Danish physicist Hans Christian Ørsted (1777–1851), who in 1820 discovered that electric currents create magnetic fields, laying the foundation for electromagnetism.[1] One oersted is defined as the magnetic field strength that exerts a force of one dyne on a unit magnetic pole in a vacuum; equivalently, 1 Oe = 1000/(4π) amperes per metre (≈ 79.58 A/m) in SI units.[2] The unit was adopted in the CGS-emu system and formally named in his honor in the 1930s.[3]

Background and Context

Role in Electromagnetism

The magnetic field strength, denoted as H⃗\vec{H}, is the component of the magnetic field that primarily determines the force exerted on a current-carrying conductor and influences the magnetization of magnetic materials within electromagnetic theory.[4] This quantity isolates the effects driven by free currents, providing a measure of the magnetizing influence independent of the material's response.[5] Historically, H⃗\vec{H} was introduced in the mid-19th century, notably by James Clerk Maxwell, to distinguish the external magnetic influence from the total magnetic induction B⃗\vec{B} observed inside materials, addressing inconsistencies in earlier models that treated magnetic fields uniformly across vacuum and matter.[5] In vacuum, H⃗\vec{H} and B⃗\vec{B} are numerically equivalent in the CGS system, but in materials, B⃗=H⃗+4πM⃗\vec{B} = \vec{H} + 4\pi \vec{M}, where M⃗\vec{M} is the magnetization, emphasizing H⃗\vec{H}'s role as the driving field.[6] A key application of H⃗\vec{H} is in calculating the force on a current-carrying wire, given by the vector equation F⃗=IL⃗×H⃗\vec{F} = I \vec{L} \times \vec{H} in CGS electromagnetic units, where II is the current in abamperes (1 abampere = 10 amperes), L⃗\vec{L} is the length vector of the wire in centimeters, and H⃗\vec{H} is in oersteds; this yields F⃗\vec{F} in dynes, ensuring unit consistency without additional constants.[7] For example, in a uniform field perpendicular to the wire, the magnitude simplifies to F=ILHF = I L H, illustrating how H⃗\vec{H} directly quantifies the mechanical interaction between currents and fields.[8] H⃗\vec{H} also plays a central role in Ampère's circuital law, which in its CGS form states ∮H⃗⋅dl⃗=4πI\oint \vec{H} \cdot d\vec{l} = 4\pi I, where II is the total enclosed current in abamperes and the integral is taken around a closed path.[9] This relation connects H⃗\vec{H} directly to the sources of magnetism—electric currents—enabling calculations of field distributions, such as H=2IrH = \frac{2I}{r} around a long straight wire or H=4πnIH = 4\pi n I inside a long solenoid with nn turns per centimeter.[7]

Distinction from Magnetic Flux Density

Magnetic flux density $ B $, measured in gauss in the CGS system, represents the total magnetic field as the amount of magnetic flux passing through a unit area perpendicular to the field.[10] In contrast, magnetic field strength $ H $, quantified in oersteds, denotes the magnetizing force or the "free" magnetic field produced by external sources such as currents, independent of the medium's response.[6] In a vacuum, where there is no magnetization, the relationship simplifies to $ B = H $, with the numerical values equal when $ B $ is in gauss and $ H $ in oersteds, reflecting the unit system's design where the permeability of free space is unity.[6] This equality highlights that in the absence of materials, the total field $ B $ is solely due to the applied field $ H $.[10] Within magnetic materials, the distinction becomes pronounced: $ B = H + 4\pi M $, where $ M $ is the magnetization (in electromagnetic units per cubic centimeter), accounting for the material's contribution to the total field.[6] Here, $ H $ remains the driving force from external sources, unaffected by the material's properties, while $ B $ incorporates both this applied field and the induced magnetization.[10] For linear isotropic media in CGS Gaussian units, the relationship generalizes to $ B = \mu H $, where $ \mu $ is the magnetic permeability, typically expressed as $ \mu = 1 + 4\pi \chi $ with $ \chi $ as the magnetic susceptibility; this underscores $ H $'s role in driving the field without including material feedback directly.[6]

Historical Development

Discovery of Electromagnetism

Hans Christian Ørsted (1777–1851) was a Danish physicist and chemist who served as a professor at the University of Copenhagen, where he conducted research influenced by early 19th-century ideas linking natural forces.[11] Ørsted's work built on philosophical notions of unity in nature, prompting him to investigate potential connections between electricity and magnetism.[11] On April 21, 1820, during a public lecture at the University of Copenhagen, Ørsted performed an experiment that unexpectedly revealed the magnetic effects of electric currents.[11] The setup involved a voltaic pile—a primitive battery consisting of stacked copper and zinc plates in an acidic electrolyte, producing approximately 15–20 volts from about 20 copper rectangles—connected to a straight metal wire.[11] A magnetic compass, with its needle aligned to Earth's magnetic field, was placed beneath the wire. When Ørsted closed the circuit to allow electric current to flow through the wire, the compass needle deflected sharply, indicating the presence of a magnetic field generated by the moving charges in the wire.[12] Reversing the battery's polarity reversed the current and the needle's deflection, while disconnecting the circuit returned the needle to its original position pointing north.[12] This simple arrangement demonstrated that electric currents produce magnetic fields, overturning the prevailing view that electricity and magnetism were unrelated phenomena.[11] Ørsted promptly documented his findings and published a pamphlet in Latin titled Experimenta circa effectum conflictus electrici in acum magneticam on July 21, 1820, which was privately circulated among European scientists.[11] The discovery ignited rapid advancements in physics: it directly inspired André-Marie Ampère to develop mathematical laws of electrodynamics within months, and it motivated Michael Faraday to explore electromagnetic induction in the 1830s.[11] Furthermore, Ørsted's observation laid the foundation for the concept of magnetic field lines, later visualized by Faraday as patterns of force surrounding current-carrying conductors.[11] This breakthrough marked the birth of electromagnetism as a unified field of study, transforming electrical science and paving the way for technologies like electric motors and generators.[12]

Naming and Standardization

The development of standardized units for magnetic field strength in the centimeter-gram-second (CGS) system began in the early 19th century, building on Hans Christian Ørsted's 1820 discovery of electromagnetism, which linked electric currents to magnetic effects.[11] In the 1830s, André-Marie Ampère and others explored quantitative measures of magnetic forces between currents, referring informally to a "unit magnetic field" as the field exerting a standard force on a unit pole or current element, though without a formalized system.[13] Carl Friedrich Gauss advanced this in 1832 by proposing an absolute measurement system for terrestrial magnetism, defining magnetic intensity in terms of centimeter, gram, and second, where the unit field strength corresponded to the force on a unit magnetic pole.[13] Wilhelm Weber extended Gauss's work in the 1850s, integrating electric and magnetic quantities into a coherent absolute system that laid the groundwork for the electromagnetic units (emu) in CGS.[13] By 1873, a committee of the British Association for the Advancement of Science formalized the CGS emu framework, defining the unit of magnetic field strength H implicitly through the unit magnetic pole (producing 1 dyne of force on an identical pole at 1 cm) and the biot (absolute ampere), but without assigning a specific name to the H unit, which was expressed as 1/(4π) unit pole per cm² in practical contexts.[14] The name "oersted" was proposed to honor Ørsted's foundational contributions. Prior to 1930, the term had been used informally for the CGS unit of magnetic reluctance, but in that year, the International Electrotechnical Commission (IEC) officially adopted "oersted" (symbol Oe) for the unit of magnetizing force H in the CGS emu system, reassigning the reluctance unit to be unnamed. This standardization ensured consistency in electromagnetic measurements, with 1 oersted defined as the field strength producing the defined force in the emu framework. In the Gaussian unit system, introduced around 1888 by Hermann von Helmholtz and Heinrich Hertz to unify electrostatic and electromagnetic units, the oersted serves as the unit for H with the same numerical value and dimensions as in emu.[13] Specifically, in vacuum, the Gaussian system sets the permeability to unity, such that the magnetic flux density B (in gauss) equals H (in oersted) numerically.[15] This integration facilitated theoretical work in electromagnetism while maintaining compatibility with the CGS emu practical applications.

Definition in CGS System

Formal Definition

In the CGS electromagnetic unit (emu) system, the oersted (Oe) is the unit of magnetic field strength $ H $, defined as the magnetic field that exerts a force of 1 dyne on a unit magnetic pole (a pole of strength 1 emu).[16][17] This definition arises from the fundamental relation $ H = F / m $, where $ F $ is the force in dynes and $ m $ is the pole strength in electromagnetic units, ensuring consistency within the emu framework used for magnetic phenomena.[16] Equivalently, the oersted can be expressed through Ampère's circuital law in the emu system, where the line integral of $ H $ around a closed path equals $ 4\pi $ times the enclosed current in emu: $ \oint \mathbf{H} \cdot d\mathbf{l} = 4\pi n I $, with $ n $ the number of turns and $ I $ the current in electromagnetic units (abamperes).[16] This formulation ties the unit directly to practical configurations like solenoids, where $ H $ inside is $ 4\pi n I / l $ (with $ l $ the length in cm), yielding 1 Oe for (1/(4π)) abamperes per cm (or 1/(4π) abampere-turns per cm) in a single-turn setup.[16] The oersted derives from base emu units of current (abampere) and length (centimeter), such that 1 Oe corresponds to (1/(4π)) emu of current per centimeter (in the context of unit turn density in a solenoid).[18] The emu system, distinct from the electrostatic unit (esu) system, is specifically employed for magnetic quantities to maintain dimensional coherence with mechanical units like the dyne and erg.[16] In vacuum, where the permeability is unity, the numerical value of $ H $ in oersteds equals that of the magnetic flux density $ B $ in gauss.[18]

Relation to Ampere-Turns

The ampere-turn (At) serves as the unit of magnetomotive force (MMF) in both SI and practical CGS contexts, representing the product of current in amperes and the number of turns in a coil, denoted as $ F_m = N I $, where $ N $ is the total number of turns and $ I $ is the current.[19] In the CGS electromagnetic system, this MMF relates directly to the magnetic field strength $ H $ (measured in oersteds, Oe) inside a solenoid or electromagnet, where $ H $ is realized as the MMF divided by the effective magnetic path length $ l $ in centimeters, providing a practical bridge from theoretical definitions to experimental measurements.[19] For a long solenoid in the CGS system, the magnetic field strength $ H $ is given by $ H = \frac{4\pi N I}{10 l} $ oersteds, where $ N $ is the total number of turns, $ I $ is the current in amperes, and $ l $ is the length of the solenoid in centimeters; this formula accounts for the conversion from practical ampere units to electromagnetic units (emu), as one abampere (the emu current unit) equals 10 amperes.[19] As an example, consider a solenoid with 1000 turns, carrying 2 amperes over a length of 50 cm: substituting into the formula yields $ H = \frac{4\pi \times 1000 \times 2}{10 \times 50} = \frac{4\pi \times 2000}{500} = 50.27 $ oersteds, illustrating how ampere-turns (here, 2000 At) scale the field strength linearly with turn density.[19] In applications involving electromagnets, ampere-turns determine the $ H $ field inside magnetic cores, such as iron or ferrite, by applying the solenoid formula to the mean magnetic path length around the core; for instance, increasing $ N I $ enhances $ H $, which in turn drives magnetization $ M $ via the core's permeability, enabling control of flux density $ B = H + 4\pi M $ in gauss.[19] This realization is essential for designing devices like relays or transformers, where precise ampere-turn calculations ensure the desired $ H $ without saturation.[19] The gilbert (Gb) acts as an intermediate CGS unit for MMF, defined such that $ H $ in oersteds equals the MMF in gilberts per centimeter of path length, with 1 oersted corresponding to 1 gilbert per centimeter; equivalently, 1 gilbert = $ \frac{10}{4\pi} $ ampere-turns, facilitating conversions between CGS and SI while distinguishing MMF from field strength per unit length.[19]

Comparison with SI Units

Conversion Factors

The oersted (Oe) is converted to the SI unit of magnetic field strength, ampere per meter (A/m), using the factor $ 1 , \mathrm{Oe} = \frac{1000}{4\pi} , \mathrm{A/m} \approx 79.577 , \mathrm{A/m} $.[20][21] This exact conversion arises from the definitions in the CGS electromagnetic system, where the oersted is defined such that one oersted produces a force of one dyne between two unit poles separated by one centimeter, scaled to SI base units.[22] For the magnetic flux density $ B $, the related CGS unit is the gauss (G), which converts to the SI unit tesla (T) as $ 1 , \mathrm{G} = 10^{-4} , \mathrm{T} $.[20] In vacuum, where the permeability is unity in CGS units, $ B = H $ numerically, so the conversion for $ H $ in oersteds aligns directly with $ B $ in gauss; for example, a field of 1 Oe corresponds to 1 G, or $ 10^{-4} , \mathrm{T} $.[22] Magnetization $ M $ in CGS units is expressed in electromagnetic units per cubic centimeter (emu/cm³), converting to SI as $ 1 , \mathrm{emu/cm^3} = 1000 , \mathrm{A/m} $.[22] In the CGS system, the relationship $ B = H + 4\pi M $ holds, with all quantities in consistent units (gauss, oersted, and emu/cm³, respectively), providing a bridge to SI equivalents after applying the above factors.[22] The following table summarizes common conversion factors between CGS and SI magnetic units, with numerical examples:
CGS UnitSI EquivalentConversion FactorExample Conversion
1 oersted (Oe)Ampere per meter (A/m)$ \frac{1000}{4\pi} \approx 79.577 $10 Oe ≈ 795.77 A/m
1 gauss (G)Tesla (T)$ 10^{-4} $1000 G = 0.1 T
1 emu/cm³ (magnetization)Ampere per meter (A/m)10000.5 emu/cm³ = 500 A/m
1 G (for 4πM)Ampere per meter (A/m)$ \frac{1000}{4\pi} \approx 79.577 $4π G ≈ 79.577 A/m (for M)
These factors facilitate direct numerical translation in calculations involving magnetic materials and fields.[22][20]

Practical Differences in Applications

The use of the oersted (Oe) in the CGS system simplifies calculations in vacuum, where the magnetic flux density $ B $ numerically equals the magnetic field strength $ H $, avoiding the SI vacuum permeability constant $ \mu_0 $.[15] This equivalence streamlines theoretical analyses in magnetism, as Gaussian CGS units render electromagnetic equations more symmetric by eliminating dimensional artifacts like $ \mu_0 $ and $ \epsilon_0 $.[15] Prior to the 1960s, the oersted dominated magnetism literature, enabling direct interpretation of historical data without immediate unit adjustments.[23] Conversely, the SI system's ampere per meter (A/m) for $ H $ ensures uniformity with electrical units like the ampere, supporting cohesive designs in electromechanical systems and adherence to global standards.[24] This integration proves beneficial for high-field applications, where explicit $ \mu_0 $ handling facilitates precise modeling in international collaborations.[24] In magnet design, CGS conventions apply oersteds to $ H $ and gauss to $ B $, with the relation $ B = H + 4\pi M $ treating permeability $ \mu $ as dimensionless and equal to 1 in vacuum.[24] SI permeability calculations, however, incorporate $ \mu = B / (\mu_0 H) $ with units of henry per meter, demanding the constant $ \mu_0 = 4\pi \times 10^{-7} $ H/m and altering relative permeability $ \mu_r $ computations for material assessments.[24] For instance, designing permanent magnets like alnico requires coercivity values in oersteds under CGS for legacy compatibility, but SI equivalents adjust for $ \mu_0 $ to align with modern energy product evaluations.[25] Transitioning legacy data from oersteds to SI poses challenges in contemporary simulations, as conversions—such as $ 1 $ Oe $ \approx 79.58 $ A/m—involve factors like $ 4\pi \times 10^{-3} $ that can propagate errors when integrating historical material properties into software like finite element analysis tools.[23][24]

Physical Implications

Energy Density in Magnetic Fields

The energy density stored in a magnetic field, denoted as $ u $, in the CGS Gaussian system is given by $ u = \frac{1}{8\pi} \mathbf{B} \cdot \mathbf{H} $ for linear isotropic media, where $ \mathbf{B} $ is the magnetic flux density in gauss and $ \mathbf{H} $ is the magnetic field strength in oersteds.[26] In vacuum, where $ \mathbf{B} = \mathbf{H} $ and the permeability $ \mu = 1 $, this simplifies to $ u = \frac{H^2}{8\pi} $, highlighting the oersted's direct role in quantifying the field's energy storage capacity per unit volume in ergs per cubic centimeter.[27] This formula arises from the work required to establish the magnetic field, derived by considering the incremental energy supplied by external currents during the field's buildup. The total magnetic energy $ W $ is obtained by integrating the differential work over the volume: $ W = \frac{1}{8\pi} \int \mathbf{H} \cdot d\mathbf{B} , dV $, where the integration path follows the magnetization process from zero field to the final state. For linear media, performing the integral yields the closed-form expression $ \frac{1}{8\pi} \mathbf{B} \cdot \mathbf{H} $. This derivation underscores the oersted as the unit measuring the "effort" (H) against which the flux (B) is built up, analogous to voltage in electrostatic energy calculations.[28] In magnetic materials, the total energy density distinguishes between contributions from the field itself and the matter. The field energy density is $ u_\text{field} = \frac{H^2}{8\pi} $, representing the energy that would be present in vacuum for the same H. The matter energy density, accounting for the interaction with magnetization $ \mathbf{M} $, is $ u_\text{matter} = \frac{1}{8\pi} \int_0^H \mathbf{H}' \cdot d(4\pi \mathbf{M}) $, where the relation $ \mathbf{B} = \mathbf{H} + 4\pi \mathbf{M} $ holds in Gaussian units. The sum $ u = u_\text{field} + u_\text{matter} $ gives the total, with the integral capturing hysteresis losses or alignment work in ferromagnets.[28] These expressions find practical application in estimating stored energy in devices like inductors and permanent magnets, where H values in oersteds directly influence calculations. For an inductor, the total energy scales with $ \frac{1}{8\pi} L I^2 $, with inductance L related to the geometry and H = (4π n I)/c in emu contexts, enabling quick assessments of energy density from coil design parameters. In permanent magnets, the maximum energy product $ (BH)_\text{max} $, with H in oersteds, quantifies the device's ability to store and deliver magnetic energy, guiding material selection for applications like motors where coercivity exceeds several thousand oersteds to maintain field integrity.[24]

Measurement Techniques

Historical measurement of magnetic field strength in oersteds relied on the flip coil method combined with a ballistic galvanometer to integrate the magnetizing force H along a path. In this technique, a small coil of known area and number of turns is placed with its plane perpendicular to the field, then rapidly flipped or withdrawn to induce a charge proportional to the change in magnetic flux, which in vacuum or air approximates H since B ≈ H in cgs units. The ballistic galvanometer measures the total charge Q passed, related to H by Q = (2 N A H)/R for the flip (where the flux change is 2 N A H), with N turns, A area, and R resistance, allowing H to be calculated in oersteds after calibration. This method was particularly useful for uniform fields in solenoids or along linear paths, providing accuracies on the order of 1% for fields up to several thousand oersteds. Modern adaptations continue to use search coils paired with electronic fluxmeters for precise measurements, outputting results in electromagnetic units (emu) that are converted to oersteds. The search coil is inserted into the field and then removed or reversed, inducing a voltage integrated by the fluxmeter to yield the flux linkage ΔΦ (e.g., N A H for removal or 2 N A H for reversal, in maxwells for air-core measurements), from which H in oersteds is derived as H = ΔΦ / (N A) adjusted for the method. These instruments achieve resolutions better than 0.1% and are suitable for fields from a few oersteds to 10,000 Oe, often employed in magnet characterization. Hall effect probes, calibrated directly in oersteds, provide a convenient modern alternative for real-time, point-wise measurements of H, especially in air where the Hall voltage V_H is proportional to H via V_H = (I B t)/(n e d) ≈ (I H t)/(n e d) since μ ≈ 1. These semiconductor-based sensors output a voltage linear with field strength, with commercial models offering ranges up to 20,000 Oe and accuracies of 0.5-1%, calibrated against known fields for cgs readout. For high magnetic fields exceeding 10,000 oersteds, nuclear magnetic resonance (NMR) or proton resonance methods are employed, exploiting the Larmor precession frequency ν of protons in the field, given by ν = (γ / 2π) H, where γ is the proton gyromagnetic ratio (42.58 MHz/T or approximately 4.258 kHz/Oe). A small sample of water or oil is placed in the field, and the resonance frequency is detected using a sweep of radiofrequency, yielding H directly in oersteds with accuracies of 10^{-4} or better, independent of probe geometry. This technique is absolute and highly precise for fields up to 50,000 Oe or more, commonly used in laboratory electromagnets. Calibration standards for these instruments typically involve long solenoids with known ampere-turns to establish a baseline of 1 oersted, where the field H = 0.4 π n I with n in turns per cm and I in amperes, ensuring traceability to fundamental electrical units. As noted in the relation to ampere-turns, this provides a reproducible reference for scaling measurements across techniques.
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