Magnetic resistance

Physical size
Surname	magnetic resistance, reluctance
Formula symbol	${\displaystyle R_{\text{m}}}$
Size and unit system unit dimension SI H −1 = A · V −1 · s −1 M −1  L −2  I 2  T 2

The magnetic resistance or reluctance is the proportionality factor between the magnetic voltage and the magnetic flux in the form: ${\displaystyle R_{\text{m}}}$ ${\displaystyle U_{\text{m}}}$ ${\displaystyle \Phi }$

${\displaystyle U_{\text{m}}=R_{\text{m}}\cdot \Phi }$

According to John Hopkinson, the equation is referred to as Hopkinson's law or Hopkin’s law and has a form similar to Ohm's law for the electrical circuit , if the magnetic flux is put in analogy to the electrical current strength and the magnetic voltage to the electrical voltage . The magnetic resistance is not to be confused with the magnetoresistive effect , which describes an electrical resistance that is influenced by a magnetic flux. ${\displaystyle \Phi }$ ${\displaystyle I}$ ${\displaystyle U_{\text{m}}}$ ${\displaystyle U}$

Due to the historical formation of the term, the magnetic voltage is sometimes referred to in the specialist literature as magnetic flux with the symbol . ${\displaystyle U_{\text{m}}}$ ${\displaystyle \Theta }$

The magnetic resistance for an element with uniform magnetic flux corresponds to the size:

${\displaystyle R_{\text{m}}={\frac {l}{\mu _{0}\cdot \mu _{\text{r}}\cdot A}}}$

This corresponds to

${\displaystyle l}$the length of the magnetic circuit in meters ,

${\displaystyle \mu _{0}}$the permeability of vacuum ( henry per meter), ${\displaystyle 4\pi \cdot 10^{-7}}$

${\displaystyle \mu _{\text{r}}}$the relative permeability of the material (dimensionless),

${\displaystyle A}$the cross-sectional area of the magnetic conductor in square meters .

_Iron core with air gap
R _m  =  R _{m, iron}  +  R _{m, air}

In the case of magnetic circuits with constant magnetic conductance values, cross-sections and lengths in sections, partial magnetic resistances can be determined according to the above relationship. The calculation rules for combining these resistances are analogous to those for connecting electrical resistors in series and in parallel .

The total resistance in the magnetic circuit is also decisive for its inductivity and magnetic flux density . ${\displaystyle L}$ ${\displaystyle B}$

Magnetic resistances are used in the magnetic circuit theory developed by John Hopkinson and his son Edward Hopkinson at the end of the 19th century. The ideas developed at that time were a basis for the construction of electrical machines and are still used today to understand simple magnetic circuits.

The reciprocal of the magnetic resistance is the magnetic conductance or permeance . ${\displaystyle G_{\text{m}}}$

The unit of magnetic resistance in the International System of Units (SI) is the reciprocal of the unit Henry and can be expressed as H ⁻¹ . The unit of magnetic conductance is Henry . ${\displaystyle R_{\text{m}}}$ ${\displaystyle G_{\text{m}}}$

See also

• magnetic flux density
• magnetic field strength
• Electromagnet
• Reluctance force
• Reluctance motor

literature

• Karl Küpfmüller, Gerhard Kohn: Theoretical electrical engineering and electronics . 14th edition. Springer, 1993, ISBN 3-540-56500-0 .