Oersted (Oe): Magnetic Field Strength in Classical Electromagnetism
The oersted (symbol Oe) expresses magnetic field strength H in the Gaussian CGS system. One oersted equals the magnetising force that would arise in vacuum if a current of 0.795 774 ampere flowed through one turn of wire per centimetre of path length. Converting to SI, 1 Oe corresponds to exactly 1000/(4π) A·m⁻¹, or about 79.577 471 A·m⁻¹. Understanding this relationship is essential when interpreting magnetisation curves, demagnetisation factors, or coercivity data published before full SI adoption.
Use this guide alongside the gauss explainer and experiment with excitation requirements using the Ohm’s law calculator to keep both H and B descriptions synchronised.
Definition and Conversions
H-field as line integral of current density
In CGS electromagnetism, magnetic field strength H is defined so that the circulation of H around a closed loop equals 4π times the enclosed current in abamperes. If a long straight conductor carries 1 abampere (equivalent to 10 A) and a circular path of radius 1 cm is chosen, the magnitude of H along that path equals 1 oersted. The CGS formulation therefore embeds the 4π factor into the unit definition. By contrast, SI rationalisation sets the circulation equal to the enclosed current in amperes, removing the geometric factor. Recognising the source of these constants helps practitioners convert between oersted and ampere per metre without losing physical meaning.
Numerical bridge to SI units
The precise conversion is 1 Oe = 1000 / (4π) A·m⁻¹. Consequently 1 A·m⁻¹ = 4π × 10⁻³ Oe. When translating historical demagnetisation curves into SI, convert both the ordinate (H) and the abscissa (B) using paired oersted-gauss and ampere-per-metre-tesla relationships. Documenting the conversion table inside laboratory notebooks, or referencing the workflow presented in the permeability article, ensures repeatability during audits or peer review.
Historical Background
Ørsted’s discovery and CGS adoption
Hans Christian Ørsted’s 1820 demonstration that electric currents deflect a compass needle unified electricity and magnetism, leading André-Marie Ampère to formulate the law of current-induced magnetic fields. The CGS system adopted the oersted in the late nineteenth century to honour this breakthrough. By defining H using abampere currents and centimetre-length loops, CGS preserved intuitive ties between laboratory apparatus and theoretical equations. Early magnetic materials research, including the work of J. A. Ewing and P. Weiss, published coercivity and magnetisation data in oersted, establishing the unit as a standard for characterising ferromagnets.
Transition to ampere-per-metre
Engineering requirements for power generation, telecommunications, and radar demanded unit coherence with mechanical quantities. The MKSA system rationalised Maxwell’s equations by eliminating redundant 4π factors, paving the way for the 1960 SI adoption of ampere-per-metre for H. Nevertheless, magnetics researchers and industries with extensive legacy datasets—such as permanent magnet manufacturing—continued quoting oersted values for decades. Contemporary datasheets often list coercivity in both kA·m⁻¹ and kOe, underlining the ongoing need for bilingual literacy.
Field Concepts and Boundary Conditions
Distinguishing H and B fields
The magnetic field strength H (measured in oersted or ampere-per-metre) characterises the magnetising force due to free currents, whereas magnetic flux density B (in gauss or tesla) includes the material response. In linear media, the relation B = µ · H applies, where µ denotes permeability. Because CGS splits µ into dimensionless and dimensional factors, the numerical relationship between Oe and G depends on material properties. Careful attention to this distinction prevents confusion when comparing CGS magnetisation curves with SI B-H plots, a topic expanded in the electric current overview.
Interface conditions in mixed units
Boundary conditions require tangential components of H to be continuous across interfaces except where surface currents exist. When modelling ferrite cores with air gaps, designers must convert oersted-based magnetising forces to ampere-per-metre before applying modern finite element solvers. Air gaps often dominate the MMF drop, so specifying H in Oe along the gap while quoting B in tesla inside the core leads to inconsistencies. Maintain a single unit system within each simulation region, then convert results for reporting—a practice mirrored in contemporary permeability standards.
Measurement Techniques
Magnetometers and field coils
Laboratory magnetometers calibrate field strength using Helmholtz coils or solenoids with precisely known turns and geometry. When legacy documentation specifies calibration currents in CGS abampere units, technicians convert the required excitation from oersted to ampere-per-metre, then compute the necessary supply voltage using Ohm’s law. Digital gaussmeters typically report B, so deriving H requires dividing by permeability. For vacuum fields, H = B / µ₀, meaning 1 Oe equals 1 G in empty space, a convenient mnemonic for cross-checking instrumentation.
Vibrating sample magnetometer workflows
Vibrating sample magnetometers (VSMs) measure magnetic moment as a function of applied field. Older instruments with analog controllers display field strength in oersted, while modern software defaults to SI units. During data reduction, researchers preserve both scales, enabling comparison with historical hysteresis loops. Export templates often include dual axes, with automatic conversion factors derived from coil calibration constants. Archiving these details satisfies quality systems aligned with ISO/IEC 17025 accreditation.
Applications Across Industries
Permanent magnet engineering
Manufacturers of NdFeB, SmCo, and ferrite magnets report intrinsic coercivity (Hci) and operating points in both kA·m⁻¹ and kOe. Designers of electric motors, actuators, and sensors frequently revisit legacy application notes that specify field strengths in oersted. Converting these limits allows accurate sizing of stator slots, back-iron thickness, and demagnetisation margins in SI-based finite element models.
Magnetic recording and spintronics
Early magnetic tape and disk technologies quoted coercive force in oersted. Modern spintronic research, including giant magnetoresistance heads and magnetic tunnel junctions, references those values when benchmarking new materials. Researchers overlay historical B-H loops with contemporary data expressed in A·m⁻¹, preserving continuity that aids patent reviews and comparative studies.
Biomedical and geophysical measurements
Biomedical magnetics, such as magnetic particle imaging and targeted hyperthermia, sometimes cite field strengths in oersted to align with earlier literature. Geophysicists interpreting magnetic anomaly surveys likewise encounter Oe-based field maps. Converting these datasets into SI ensures compatibility with modelling tools that calculate torque, energy, or induced currents using ampere-per-metre conventions.
Importance and Continuing Relevance
Standards and compliance
Regulatory documents, including military specifications for permanent magnets and aerospace magnetic cleanliness requirements, often reference oersted thresholds. Maintaining dual reporting in Oe and A·m⁻¹ demonstrates compliance with both legacy and modern specifications. Aligning notation with ISO 80000-6 and referencing permeability measurements strengthens traceability for certification audits.
Education and interdisciplinary communication
Students encounter oersted while studying magnetostatics, while practicing engineers rely on ampere-per-metre for design calculations. Providing both perspectives cultivates interdisciplinary fluency. Teaching materials often pair textbook derivations in CGS with computational assignments in SI, encouraging learners to verify results using tools such as the Ohm’s law voltage calculator and the LC resonance tool to bridge theoretical and practical views of magnetic excitation.
Mastering the oersted keeps historic research, industrial experience, and modern modelling aligned. By carefully converting between CGS and SI, teams safeguard data integrity and accelerate innovation across magnetics-heavy sectors.