μ₀ measures how easily a magnetic field forms in vacuum. Together with ε₀ it fixes the speed of light.
Value of μ₀ in different units
| Value | Use it when |
|---|---|
| 4π × 10⁻⁷ T m A⁻¹ (or H/m) | Exact before 2019, still used in all exams. |
| 1.257 × 10⁻⁶ N A⁻² | Decimal form. |
| 10⁻⁷ T m A⁻¹ (μ₀/4π) | The form that appears in Biot–Savart. |
Formulas that use μ₀
- B = μ₀I/2πr (long wire)
- B = μ₀nI (solenoid)
- dB = (μ₀/4π) I dl sin θ/r²
- c = 1/√(μ₀ε₀)
Its dimensional formula is worked out on the dimensional formula of permeability of free space μ₀ page.
Other constants
- Gas constant (R): 8.314 J mol⁻¹ K⁻¹
- Planck's constant (h): 6.626 × 10⁻³⁴ J s
- Avogadro's number (Nₐ): 6.022 × 10²³ mol⁻¹
- Speed of light (c): 3 × 10⁸ m/s
- Charge of an electron (e): 1.602 × 10⁻¹⁹ C
- Mass of an electron (mₑ): 9.109 × 10⁻³¹ kg
- Mass of a proton (mₚ): 1.673 × 10⁻²⁷ kg
- Mass of a neutron (mₙ): 1.675 × 10⁻²⁷ kg
- Universal gravitational constant (G): 6.674 × 10⁻¹¹ N m² kg⁻²
- Acceleration due to gravity (g): 9.8 m/s²
- Boltzmann constant (k): 1.381 × 10⁻²³ J/K
- Faraday constant (F): 96 485 C/mol
- Permittivity of free space (ε₀): 8.854 × 10⁻¹² C² N⁻¹ m⁻²
- Permeability of free space (μ₀): 4π × 10⁻⁷ T m/A
- Rydberg constant (R): 1.097 × 10⁷ m⁻¹
- Stefan–Boltzmann constant (σ): 5.67 × 10⁻⁸ W m⁻² K⁻⁴
- Wien's constant (b): 2.898 × 10⁻³ m K
- Bohr radius (a₀): 0.529 Å
- Molar volume of a gas at STP (Vₘ): 22.4 L/mol
The full list, searchable, is on the physical constants page.
Questions students ask
What is the value of permeability of free space?
μ₀ = 4π × 10⁻⁷ T m/A. In other units: 4π × 10⁻⁷ T m A⁻¹ (or H/m); 1.257 × 10⁻⁶ N A⁻²; 10⁻⁷ T m A⁻¹ (μ₀/4π).
What is μ₀ in physics and chemistry?
μ₀ measures how easily a magnetic field forms in vacuum. Together with ε₀ it fixes the speed of light.
Which value of μ₀ should I use?
4π × 10⁻⁷ T m A⁻¹ (or H/m): Exact before 2019, still used in all exams. 1.257 × 10⁻⁶ N A⁻²: Decimal form. 10⁻⁷ T m A⁻¹ (μ₀/4π): The form that appears in Biot–Savart.
What is the dimensional formula of permeability of free space?
See the dimensional formula of permeability of free space, worked out step by step on its own page.