Magnetic complex reluctance (SI Unit: H⁻¹) is a measurement of a passive magnetic circuit

Magnetic circuit

A magnetic circuit is made up of one or more closed loop paths containing a magnetic flux. The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials like iron, although there may be air gaps or other...

 (or element within that circuit) dependent on sinusoidal magnetomotive force (SI Unit: At

Ampere-turn

The ampere-turn was the MKS unit of magnetomotive force , represented by a direct current of one ampere flowing in a single-turn loop in a vacuum...

·Wb

Weber

Weber is a surname of German origin, derived from the noun meaning "weaver". In some cases, following migration to English-speaking countries, it has been anglicised to the English surname 'Webber' or even 'Weaver'.Notable people with the surname include:...

⁻¹) and sinusoidal magnetic flux

Magnetic flux

Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...

 (SI Unit: T

Tesla (unit)

The tesla is the SI derived unit of magnetic field B . One tesla is equal to one weber per square meter, and it was defined in 1960 in honour of the inventor, physicist, and electrical engineer Nikola Tesla...

·m

Metre

The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

²), and this is determined by deriving the ratio of their complex effective amplitudes.[Ref. 1-3]

As seen above, magnetic complex reluctance is a phasor

Phasor

Phasor is a phase vector representing a sine wave.Phasor may also be:* Phasor , a stereo music, sound and speech synthesizer for the Apple II computer* Phasor measurement unit, a device that measures phasors on an electricity grid...

 represented as uppercase Z mu where:

and represent the magnetomotive force (complex effective amplitude)

and represent the magnetic flux (complex effective amplitude)

, lowercase z mu, is the real part of magnetic complex reluctance

The "lossless" magnetic reluctance

Magnetic reluctance

Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is analogous to resistance in an electrical circuit, but rather than dissipating magnetic energy it stores magnetic energy...

, lowercase z mu, is equal to the absolute value (modulus) of the magnetic complex reluctance. The argument distinguishing the "lossy" magnetic complex reluctance from the "lossless" magnetic reluctance is equal to the natural number raised to a power equal to:

Where:

• is the imaginary number
• is the phase of the magnetomotive force
• is the phase of the magnetic flux
• is the phase difference

The "lossy" magnetic complex reluctance represents a magnetic circuit element's resistance to not only magnetic flux but also to changes in magnetic flux. When applied to harmonic regimes, this formality is similar to Ohm's Law

Ohm's law

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...

 in ideal AC circuits. In magnetic circuits, magnetic complex reluctance equal to:


Where:

• is the length of the circuit element
• is the cross-section of the circuit element
• is the complex magnetic permeability
  Permeability (electromagnetism)
  In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...