## Magnetic Permeability

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:

μr = Relative Magnetic Permeability (dimensionless)

μ = Any Given Magnetic Permeability (H/m)

μo = 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 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:

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 (µo) 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.

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