Magnetic permeability:

$$\mu= \frac{B}{H}$$

Where:

$\mu$μ = Magnetic Permeability (Henries/meter)

B = Magnetic Flux Density (Tesla)

H = Magnetizing Force

 (Am/meter)

Relative Magnetic Permeability:

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

Where:

μ_r = Relative Magnetic Permeability (dimensionless)

μ = Any Given Magnetic Permeability (H/m)

μ_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 4π 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 µ_o.

In engineering applications, permeability

 is often expressed in relative, rather than in absolute

, terms. If µ_o 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

, µ_r, 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:

Example 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.

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

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

$$\mu_{r}=44.78$$

Example 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 (µ_o) of 1.257x10^-6 H/mm Rearranging this equation to solve for absolute

 permeability

 results in:

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

$$\mu=\mu_{r}\mu_{0}$$

Plugging the given values into the equation produces an absolute

 permeability

 value.

$$\mu=1.05\times1.257\times10^{-6}$$