Magnetic capacitivity

Magnetic capacitivity (SI Unit: H) is a component used in the gyrator-capacitor model of magnetic systems.

This element, denoted as $C_\mathrm{M}$, is an extensive property and is defined as:

$C_\mathrm{M} = \mu_\mathrm{r} \mu_0\frac{S}{l}$

Where: $\mu_\mathrm{r} \mu_0 = \mu$ is the magnetic permeability, $S$ is the element cross-section, and $l$ is the element length.

For phasor analysis, the magnetic permeability^[1] and the magnetic capacitivity are complex values.^[1][2]

Magnetic capacitivity is also equal to magnetic flux divided by the difference of magnetic potential across the element.

$C_\mathrm{M} = \frac{\Phi}{\phi_\mathrm{M1}-\phi_\mathrm{M2}}$

Where:

$\phi_\mathrm{M1}-\phi_\mathrm{M2}$ is the difference of the magnetic potentials.

The notion of magnetic capacitivity is employed in the gyrator-capacitor model in a way analogous to capacitance in electrical circuits.

References

Arkadiew W. Eine Theorie des elektromagnetischen Feldes in den ferromagnetischen Metallen. – Phys. Zs., H. 14, No 19, 1913, S. 928-934.</ref>

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1. Arkadiew W. Eine Theorie des elektromagnetischen Feldes in den ferromagnetischen Metallen. – Phys. Zs., H. 14, No 19, 1913, S. 928-934.
2. Popov V. P. The Principles of Theory of Circuits. – M.: Higher School, 1985, 496 p. (In Russian).