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Constants library

12 values, each with its units, its uncertainty, and where it came from.

Electromagnetic 12

Vacuum magnetic permeability measured

μ0=0.00000125663706127 N/A2 (H/m)\mu_{0} = 0.00000125663706127\ \text{N/A}^{2}\text{ (H/m)}

N/A² (H/m)How strongly a current magnetises empty space — the constant in Ampère's law, no longer exactly 4π×10⁻⁷ since the 2019 SI redefinition.

Bohr magneton measured

μB=9.2740100657×10−24 J/T\mu_{\mathrm{B}} = 9.2740100657 \times 10^{-24}\ \text{J/T}

J/TThe natural quantum of magnetic moment for an electron, eħ/2mₑ — the yardstick for atomic magnetism and electron spin.

Nuclear magneton measured

μN=5.0507837393×10−27 J/T\mu_{\mathrm{N}} = 5.0507837393 \times 10^{-27}\ \text{J/T}

J/TThe magnetic-moment unit for nuclei, eħ/2mₚ — smaller than the Bohr magneton by the full proton-to-electron mass ratio of 1836.

Electron magnetic moment measured

μe=−9.2847646917×10−24 J/T\mu_{\mathrm{e}} = -9.2847646917 \times 10^{-24}\ \text{J/T}

J/TThe magnetic moment of a free electron, negative because its charge is, and about 0.116% larger than one Bohr magneton.

Proton magnetic moment measured

μp=1.41060679545×10−26 J/T\mu_{\mathrm{p}} = 1.41060679545 \times 10^{-26}\ \text{J/T}

J/TThe magnetic moment of the proton, 2.79 nuclear magnetons rather than the 1 a point particle would show — evidence of quark structure.

Neutron magnetic moment measured

μn=−9.6623653×10−27 J/T\mu_{\mathrm{n}} = -9.6623653 \times 10^{-27}\ \text{J/T}

J/TA neutral particle with a magnetic moment of −1.913 nuclear magnetons — proof on its own that the neutron has charged internal structure.

Proton gyromagnetic ratio measured

γp=267522187.08 s−1⋅T−1\gamma_{\mathrm{p}} = 267522187.08\ \text{s}^{-1}{\cdot}\text{T}^{-1}

s⁻¹·T⁻¹The proton's precession rate per unit magnetic field in angular frequency — the constant that turns a magnet strength into an NMR frequency.

Proton gyromagnetic ratio over 2π measured

γp/2π=42577478.461 Hz/T\gamma_{\mathrm{p}}/2\pi = 42577478.461\ \text{Hz/T}

Hz/TThe proton Larmor frequency per tesla, 42.577 MHz/T — the number every NMR spectroscopist and MRI physicist works in directly.

Electron gyromagnetic ratio measured

γe=1.76085962784×1011 s−1⋅T−1\gamma_{\mathrm{e}} = 1.76085962784 \times 10^{11}\ \text{s}^{-1}{\cdot}\text{T}^{-1}

s⁻¹·T⁻¹The electron's spin precession rate per tesla, 658 times the proton's — the basis of electron spin resonance and of spin-qubit control.

Relative permeability of iron measured

μr,Fe=5000 —\mu_{r,\mathrm{Fe}} = 5000\ \text{—}

—Typical maximum relative permeability of commercial soft iron — a wildly variable figure spanning roughly 200 to 5000 with purity and field level.

Relative permeability of mu-metal measured

μr,μ-metal=80,000 —\mu_{r,\mu\text{-metal}} = 80,000\ \text{—}

—Typical relative permeability of annealed mu-metal in weak fields — the nickel-iron alloy used to shield instruments from stray magnetic fields.

Earth's magnetic field strength measured

B⊕=0.00005 TB_{\oplus} = 0.00005\ \text{T}

TTypical magnitude of the geomagnetic field at the surface, near 50 μT but ranging from about 25 μT at the equator to 65 μT near the poles.