Magnetic capacitance

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 and the magnetic capacitivity are complex values.

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.