Magnetic complex reluctance

Articles about
Electromagnetism
Electricity Magnetism Optics History Computational Textbooks Phenomena
Electrostatics Charge density Conductor Coulomb law Electret Electric charge Electric dipole Electric field Electric flux Electric potential Electrostatic discharge Electrostatic induction Gauss law Insulator Permittivity Polarization Potential energy Static electricity Triboelectricity
Magnetostatics Ampère law Biot–Savart law Gauss magnetic law Magnetic dipole Magnetic field Magnetic flux Magnetic scalar potential Magnetic vector potential Magnetization Permeability Right-hand rule
Electrodynamics Bremsstrahlung Cyclotron radiation Displacement current Eddy current Electromagnetic field Electromagnetic induction Electromagnetic pulse Electromagnetic radiation Faraday law Jefimenko equations Larmor formula Lenz law Liénard–Wiechert potential London equations Lorentz force Maxwell equations Maxwell tensor Poynting vector Synchrotron radiation
Electrical network Alternating current Capacitance Current density Direct current Electric current Electric power Electrolysis Electromotive force Impedance Inductance Joule heating Kirchhoff laws Network analysis Ohm law Parallel circuit Resistance Resonant cavities Series circuit Voltage Watt Waveguides
Magnetic circuit AC motor DC motor Electric machine Electric motor Gyrator–capacitor Induction motor Linear motor Magnetomotive force Permeance Reluctance (complex) Reluctance (real) Rotor Stator Transformer
Covariant formulation Electromagnetic tensor Electromagnetism and special relativity Four-current Four-potential Mathematical descriptions Maxwell equations in curved spacetime Relativistic electromagnetism Stress–energy tensor
Scientists Ampère Biot Coulomb Davy Einstein Faraday Fizeau Gauss Heaviside Helmholtz Henry Hertz Hopkinson Jefimenko Joule Kelvin Kirchhoff Larmor Lenz Liénard Lorentz Maxwell Neumann Ohm Ørsted Poisson Poynting Ritchie Savart Singer Steinmetz Tesla Thomson Volta Weber Wiechert
v t e

Magnetic complex reluctance (SI Unit: H⁻¹) is a measurement of a passive magnetic circuit (or element within that circuit) dependent on sinusoidal magnetomotive force (SI Unit: At·Wb⁻¹) and sinusoidal magnetic flux (SI Unit: T·m²), and this is determined by deriving the ratio of their complex effective amplitudes.[Ref. 1-3] $${\displaystyle Z_{\mu }={\frac {\dot {N}}{\dot {\Phi }}}={\frac {{\dot {N}}_{m}}{{\dot {\Phi }}_{m}}}=z_{\mu }e^{j\phi }}$$

As seen above, magnetic complex reluctance is a phasor represented as uppercase Z mu where:

• ${\displaystyle {\dot {N}}}$ and ${\displaystyle {\dot {N}}_{m}}$ represent the magnetomotive force (complex effective amplitude)
• ${\displaystyle {\dot {\Phi }}}$ and ${\displaystyle {\dot {\Phi }}_{m}}$ represent the magnetic flux (complex effective amplitude)
• ${\displaystyle z_{\mu }}$, lowercase z mu, is the real part of magnetic complex reluctance

The "lossless" magnetic reluctance, 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 ${\displaystyle e}$ raised to a power equal to: $${\displaystyle j\phi =j\left(\beta -\alpha \right)}$$ Where:

• ${\displaystyle j}$ is the imaginary number
• ${\displaystyle \beta }$ is the phase of the magnetomotive force
• ${\displaystyle \alpha }$ is the phase of the magnetic flux
• ${\displaystyle \phi }$ 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 in ideal AC circuits. In magnetic circuits, magnetic complex reluctance is equal to: $${\displaystyle Z_{\mu }={\frac {1}{{\dot {\mu }}\mu _{0}}}{\frac {l}{S}}}$$ Where:

• ${\displaystyle l}$ is the length of the circuit element
• ${\displaystyle S}$ is the cross-section of the circuit element
• ${\displaystyle {\dot {\mu }}\mu _{0}}$ is the complex magnetic permeability