Permeability Calculation

μ r = μ μ 0 \mu_{r}= \frac{\mu}{\mu_{0}}

Where:

μ \mu r = Relative Magnetic Permeability (dimensionless)

μ \mu = Any Given Magnetic Permeability (H/m)

μ \mu o = Magnetic Permeability in Free Space (H/m), which is 1.257 x 10-6 H/m

Magnetic permeability is the ease with which a material can be magnetized. It is a constant of proportionality that exists between magnetic induction and magnetic field intensity. This constant is equal to approximately 4 π \pi x10-7 henry per meter or 1.257 x 10-6 H/m in free space (a vacuum). In other materials permeability can be much different, often substantially greater than the free-space value, which is symbolized µo.

In engineering applications, permeability is often expressed in relative, rather than in absolute, terms. If µo represents the permeability of free space and µ represents the permeability of the substance in question (also specified in henrys per meter), then the relative permeability, µr, is given by the equation above. Relative permeability is dimensionless since it is the ratio of two permeability values expressed in the same units.

Examples:

1) What is the relative permeability of a material with an absolute permeability of 5.63x10-5H/m?

Simply plug the materials permeability and the free space permeability values in the equation and solve.

μ r = μ μ 0 \mu_{r}= \frac{\mu}{\mu_{0}}

μ r = 5.63 × 10 − 5 1.257 × 10 − 6 \mu_{r}=\frac{5.63\times10^{-5}}{1.257 \times 10{-6}}

μ r = 44.78 \mu_{r}=44.78

2) What is the absolute permeability of a materials with a relative permeability of 1.05

Given the equation and the permeability of free space (µo) of 1.257x10-6 H/mm Rearranging this equation to solve for absolute permeability results in:

μ r = μ μ 0 \mu_{r}= \frac{\mu}{\mu_{0}}

μ = μ r μ 0 \mu=\mu_{r}\mu_{0}

Plugging the given values into the equation produces an absolute permeability value.

μ = 1.05 × 1.257 × 10 − 6 \mu=1.05\times1.257\times10^{-6}

μ = 1.32 × 10 − 6 \mu=1.32\times10^{-6} H/m