The Maxwell (Mx): Legacy CGS Unit of Magnetic Flux

The maxwell (Mx) served as the CGS unit of magnetic flux for decades before the SI’s adoption of the weber. Legacy literature, geophysical archives, and astrophysics catalogues still cite flux in maxwells, making it essential for modern engineers to convert values accurately. This article defines the unit, explains its role in Gaussian and electromagnetic CGS systems, and demonstrates how to reconcile historical datasets with today’s SI-focused tools.

Definition and Conversion

Magnetic flux Φ equals the surface integral of magnetic flux density B over an oriented area A. In the Gaussian CGS system, B is measured in gauss and A in square centimetres, yielding flux in maxwells. By definition:

1 Mx = 1 G·cm² = 10⁻⁸ Wb.

Because the CGS system treats electric and magnetic quantities differently from SI, conversion factors often involve powers of ten and factors of c (the speed of light). When translating Mx values into webers, multiply by 10⁻⁸. Conversely, to express an SI flux in maxwells, multiply by 10⁸. Always document the conversion explicitly when digitising archival data to avoid sign or scale errors in derived quantities such as inductance and electromotive force.

Historical Development

Origins in the centimetre–gram–second system

During the late 19th century, physicists debated how to rationalise electromagnetic units. The British Association for the Advancement of Science promoted the CGS system, naming its magnetic flux unit after James Clerk Maxwell to honour his unifying field equations. Although early proposals also considered the name “line,” the maxwell gained consensus in the 1900s as electrical engineering expanded.

Transition to the weber

The International Electrotechnical Commission adopted the MKSA system in the 1930s, leading to the modern SI. Engineers favoured the weber because it aligned flux dimensions with volt-seconds, simplifying Faraday’s law computations. After the 1960 CGPM formalised the SI, new standards phased out the maxwell, but the conversion persisted in textbooks and research notes, particularly in magnetics, astrophysics, and geophysics.

Continuing presence in scientific literature

Solar physics still reports sunspot and solar loop flux in maxwells (e.g., 10²¹ Mx), and some geophysical surveys cite crustal magnetic anomalies using CGS units. Maintaining fluency in Mx ensures compatibility with these references and facilitates integration into SI-centric simulation tools.

Conceptual Considerations

Flux linkage and inductance

Inductance L relates total flux linkage Λ to current I via Λ = L·I. In CGS, Λ may be expressed in maxwell-turns, whereas SI uses weber-turns. When converting historical transformer data, apply ΛSI = ΛCGS × 10⁻⁸ to ensure inductance values align with henries. The LC resonant frequency calculator can then operate with SI parameters without hidden scaling factors.

Faraday’s law comparisons

Faraday’s law in differential form, ∇ × E = −∂B/∂t, is dimensionally consistent across unit systems, but the constants within Maxwell’s equations differ. Gaussian CGS embeds the speed of light c into the relationships between electric and magnetic fields, while SI introduces ε₀ and μ₀. When translating experiments from CGS to SI, confirm whether reported quantities include c factors and adjust accordingly so induced voltage calculations remain accurate.

Magnetic field mapping

Mapping flux through irregular geometries requires integrating B over the surface. Historical atlases sometimes tabulate orthogonal field components (Bx, By, Bz) in gauss. Use the vector magnitude calculator to combine components before integration, then convert the resulting Mx to webers for compatibility with modern finite element solvers.

Measurement Techniques

Search coils and fluxmeters

Search coils still provide a bridge between historical and modern units. When a coil with N turns and area A experiences a changing magnetic flux, the induced voltage is proportional to −N·dΦ/dt. Instruments calibrated in webers may display volt-seconds; multiplying by 10⁸ expresses the result in maxwell-seconds for comparison with CGS-era documents. Careful calibration against SI standards ensures long-term traceability.

Magnetograph archives

Historical magnetographs recorded solar magnetic fields onto photographic plates, later digitised as Mx per pixel. Converting these archives to SI involves not only scaling by 10⁻⁸ but also correcting for telescope aperture and plate calibration. Documenting the conversion methodology preserves scientific reproducibility when correlating with modern spacecraft measurements reported in webers.

Laboratory notes and data governance

When updating laboratory information management systems (LIMS), tag each dataset with its originating unit system. Scripts that ingest legacy CSV files should explicitly multiply or divide by 10⁸ as appropriate. Version control and metadata fields prevent subtle errors from propagating through simulation workflows or quality audits.

Applications and Use Cases

Astrophysics and solar research

Solar physicists quantify magnetic flux through sunspots, coronal loops, and active regions using maxwells, reflecting decades of CGS tradition. For example, a typical active region might exhibit 10²¹ Mx. Translating these figures to SI (10¹³ Wb) enables comparison with magnetohydrodynamic simulations and spacecraft magnetometer data delivered in webers.

Magnetic recording and materials science

Early magnetic recording standards referenced Mx to describe flux per recording track width. When analysing archival tape specifications or legacy hard-drive patents, converting to SI clarifies compatibility with modern head materials and write currents evaluated using Ohm’s law tools.

Geophysics and archaeomagnetism

Archaeomagnetic studies often cite remanent magnetisation in terms aligned with Mx units. When integrating with present-day geomagnetic surveys that use tesla and weber units, apply consistent conversions to maintain chronological comparisons of Earth’s field intensity.

Importance for Data Integrity

Misinterpreting maxwells as webers or vice versa introduces eight orders of magnitude of error—enough to invalidate electromagnetic designs or mischaracterise solar events. Document unit conversions in calculation notes, include unit metadata within datasets, and annotate axes on charts with both CGS and SI symbols when necessary. Adhering to ISO 80000 notation (using thin spaces and centred dots) keeps interdisciplinary teams aligned.

Whenever possible, phase out CGS units in new work by reporting primary results in webers while retaining maxwell values parenthetically for comparison. This practice eases collaboration with SI-focused stakeholders and supports automation in software platforms that assume SI coherence.

Where to Go Next

Bridge CGS and SI electromagnetic analyses with these resources: