Formula and Method for Magnetic Permeability
Magnetic permeability describes how easily a material supports the formation of a magnetic field within itself. It is defined as the ratio of magnetic flux density B (in tesla) to magnetic field strength H (in amperes per meter): μ = B / H, measured in henries per meter (H/m). Dividing μ by the permeability of free space, μ0 = 4π × 10⁻⁷ H/m, gives the dimensionless relative permeability, μr = μ / μ0, which tells you how many times more (or less) magnetic a material is than a vacuum.
Understanding the formula
B (magnetic flux density) and H (magnetic field strength) are related by B = μH, so measuring both at the same point in a material lets you solve directly for μ = B/H. The relative permeability μr = μ/μ0 strips out the vacuum baseline, and the closely related magnetic susceptibility, χm = μr − 1, measures how strongly a material magnetizes in response to an applied field: χm is negative (though tiny) for diamagnetic materials, slightly positive for paramagnetic materials, and large and positive for ferromagnetic materials like iron, nickel, and cobalt.
Working with units
- Magnetic flux density (B) is measured in tesla (T) in SI, or gauss (G) in the older CGS system, where 1 G = 10⁻⁴ T
- Magnetic field strength (H) is measured in amperes per meter (A/m) in SI, or oersted (Oe) in CGS, where 1 Oe = 1000/(4π) A/m ≈ 79.577 A/m
- Mixing SI and CGS units without converting is the most common source of order-of-magnitude errors in permeability calculations — always convert both B and H to consistent units before dividing
Knowing the limits
For linear materials (vacuum, air, most diamagnetic and paramagnetic substances), permeability is essentially constant regardless of field strength. For ferromagnetic materials, however, μ = B/H is not a fixed material constant — it varies with H, rises to a peak, and then falls as the material saturates at high field strengths, and it also depends on magnetic history (hysteresis). Treat any ferromagnetic permeability result as valid only at the specific B-H operating point you measured, and consult the manufacturer's B-H curve for design work.
Frequently Asked Questions
What is the difference between absolute and relative permeability?
What are typical relative permeability values?
Why does permeability change with field strength for materials like iron?
How do I convert oersted to A/m?
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Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |