The Tesla (T): Unit of Magnetic Flux Density

Overview

The tesla (T) is the SI derived unit of magnetic flux density B. ISO 80000‑6 standardizes the quantity symbol B and the unit symbol T. By definition,

1 T = 1 Wb·m⁻² = 1 N·(A⁻¹·m⁻¹) = 1 kg·s⁻²·A⁻¹.

Magnetic flux Φ is measured in weber (Wb), with Φ = ∫ B · dA. The tesla quantifies how strongly a magnetic field couples to moving charges and currents. Reference the ampere guide for current-field relationships and the volt explainer for induced EMF discussions.

Historical Development and Formalization

From cgs fields to SI magnetic units

Magnetism long used cgs units (gauss, oersted), complicating electromagnetism’s equations with conversion factors. The SI rationalization unified electric and magnetic quantities; in 1960 the 11th CGPM adopted the tesla (for Nikola Tesla) for flux density and the weber for flux. The SI expresses Lorentz force F = q·v × B and force on a conductor F = I·ℓ × B coherently. After 2019, constants e, h, and c are fixed; the magnetic constant μ₀ is now a measured quantity (no longer exact), refining how B relates to field strength H in vacuum through B = μ₀ H. Compare this evolution with the ohm's quantum-Hall realization to appreciate how magnetic phenomena underpin electrical standards.

Conceptual Foundations

B, H, M, and material response

In matter,

B = μ₀ (H + M),

where M is magnetization (A·m⁻¹). Linear isotropic materials use B = μ₀ μ_r H with relative permeability μ_r. The tesla measures B, the total flux density (applied field plus material response). Magnetic flux Φ links fields to induction: Faraday’s law

∮ E · dℓ = − dΦ/dt

underpins transformers, generators, and inductors. In mechanics, torque on a loop is τ = m × B with magnetic moment m. Reinforce these relations with the LC resonant frequency calculator and by reviewing the ISO 80000-3 space and time conventions that govern angular velocity in rotating machines.

Coherence with SI

SI avoids legacy constants: F = q·v·B (with orthogonality) yields newtons directly; induced EMF U = −dΦ/dt yields volts; energy density in vacuum u = B²/(2 μ₀) yields joules per cubic metre. Tie this coherence to the volt discussion and the ohm analysis to maintain unit consistency across electromagnetic simulations.

Realization, Calibration, and Traceability

Primary routes and instrumentation

• NMR teslametry: The Larmor frequency f = γ B/(2π) of nuclei (e.g., protons) provides an absolute measure of B when γ is known; this is a primary route for high-accuracy fields.
• Coil and fluxmeter methods: A search coil in a changing field produces voltage U = −N·dΦ/dt; integrating yields ΔΦ, and with known area A gives B.
• Hall probes and magnetoresistive sensors: Offer wide-range, direct B-sensing; calibration against NMR or coil standards controls offset, sensitivity, and temperature dependence.
• Rotating coils and stretched-wire systems: Map field harmonics and integrated gradients in accelerator magnets.

Measurement considerations

• Alignment and averaging: B is vectorial; angular misalignment and spatial inhomogeneity require cosine corrections and mapping.
• Temperature and drift: Sensor coefficients and magnet aging produce drift; active stabilization and periodic calibration mitigate it.
• Demagnetizing factors: Finite samples alter internal B/H; account for geometry when inferring material properties.
• Hysteresis and eddy currents: Excitation history affects steel cores; ramp rates and waveform shape matter for repeatability.

Use calculators like the voltage divider tool to condition Hall sensor outputs and the solar storm radiation dose calculator when relating space-weather indices to real-world B-field changes.

Applications

Medical imaging and biophysics

MRI systems operate at 1.5 T, 3 T, and higher for research (7 T+). Uniformity (shimming), stability, and gradient calibration are specified directly in teslas and T·m⁻¹. Match these requirements with calculators covering resonance—such as the LC resonant frequency solver —when planning RF excitation hardware.

Power and motion

Transformers, inductors, and motors are designed by limiting peak B to avoid core saturation. Permanent-magnet motors leverage high-B rare-earth materials; air-gap flux density sets torque density. Integrate these insights with the ohm guidance and calculators like the Ohm's Law Power tool to balance copper loss, voltage, and magnetic loading.

Particle accelerators and beamlines

Dipole and quadrupole magnets specify field and gradient in T and T·m⁻¹. Field quality (harmonics) dictates beam dynamics; rotating-coil metrology ensures compliance. Compare these requirements with the volt article for induced voltage control and the ISO 80000-10 atomic and nuclear physics overview for accelerator terminology.

Earth and space sciences

The Earth’s field is tens of µT; magnetotellurics, paleomagnetism, and space-weather monitoring quantify disturbances in teslas (or submultiples), enabling global comparability of data. Couple these studies with the solar storm radiation dose calculator to interpret geomagnetic indices in practical units.

Nondestructive evaluation and manufacturing

Magnetic particle inspection, eddy-current testing, and magnetic separation processes rely on calibrated B-fields for sensitivity and throughput. Compare these workflows with the ohm article and the ISO 80000-5 thermodynamics summary when thermal effects intersect with magnetic processes.

Why the Tesla Matters

The tesla links magnetic fields to force, induction, and energy in a way that is coherent with all other SI units. ISO 80000‑6 fixes symbols and nomenclature so results are portable across disciplines. With NMR-based primaries and well-characterized sensors, industries from healthcare to transportation and basic science can measure, compare, and regulate magnetic fields with confidence—whether designing an MRI scanner, stabilizing a particle beam, or monitoring geomagnetic storms. Pair this conclusion with the volt, ohm, and ampere articles plus calculators like the LC resonant frequency solver to ensure electromagnetic analyses remain synchronized across the site.